11
11

Apr 5, 2021
04/21

by
(MathterMaker)

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This graphing manipulative will allow students, teachers, mathematicians, or anyone else to show graphs or multiple equations by moving around disks. Graph multiple equations by printing two sets of disks in different colors. Currently small. If wanted, I could upload a 10X10 or larger. You can use it as a 3-D graph if you stack multiple disks of the same color on top of each other. Comment if you would like a more robust 3-D graphing solution.

Topics: class, pin, variable, useful, Math, tan, sin, board, multivariable, intercept, MatherMaker,...

11
11

Apr 5, 2021
04/21

by
(SimonGregg)

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These abc tiles are something that both primary / elementary and secondary / high school children can use to understand algebra. With three simple tiles algebra makes immediate sense, and they look good too.

Topics: thingiverse, Math, MakerBotAcademyMath, math, stl, algebra

11
11

Apr 5, 2021
04/21

by
(dorif)

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3D Printed Like Terms Blocks which demonstrate to students that only like terms can be combined.

Topics: thingiverse, Math, MakerBotAcademyMath, manipulatives, math, stl, xrds, algebra

854
854

Sep 7, 2018
09/18

by
1969

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Curso de Geometría analítica de N. Efimov

Topics: Editorial MIR, Álgebra, Geometría analítica

1,183
1.2K

Feb 21, 2020
02/20

by
3Blue1Brown

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3blue1brown, by Grant Sanderson, is some combination of math and entertainment, depending on your disposition. The goal is for explanations to be driven by animations and for difficult problems to be made simple with changes in perspective. Contact and FAQ: https://www.3blue1brown.com/faq

Topics: youtube, video, math, linear algebra, calculus

48
48

Jun 30, 2018
06/18

by
A Abbas; A Assi; Pedro A Garcıa-Sánchez

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Let K be a field and denote by K[t], the polynomial ring with coefficients in K. Set A = K[f1,. .. , fs], with f1,. .. , fs $\in$ K[t]. We give a procedure to calculate the monoid of degrees of the K algebra M = F1A + $\times$ $\times$ $\times$ + FrA with F1,. .. , Fr $\in$ K[t]. We show some applications to the problem of the classification of plane polynomial curves (that is, plane algebraic curves parametrized by polynomials) with respect to some oh their invariants, using the module of...

Topics: Algebraic Geometry, Commutative Algebra, Mathematics

Source: http://arxiv.org/abs/1703.02825

6
6.0

Jun 28, 2018
06/18

by
A M Semikhatov; I Yu Tipunin

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For the quantum walled Brauer algebra, we construct its Specht modules and (for generic parameters of the algebra) seminormal modules. The latter construction yields the spectrum of a commuting family of Jucys--Murphy elements. We also propose a Baxterization prescription; it involves representing the quantum walled Brauer algebra in terms of morphisms in a braided monoidal category and introducing parameters into these morphisms, which allows constructing a "universal transfer...

Topics: Quantum Algebra, Mathematics

Source: http://arxiv.org/abs/1512.06994

7
7.0

Jun 29, 2018
06/18

by
A V Jayanthan; N Narayanan; S Selvaraja

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Let $G$ be a finite simple graph and $I(G)$ denote the corresponding edge ideal. For all $s \geq 1$, we obtain upper bounds for reg$(I(G)^s)$ for bipartite graphs. We then compare the properties of $G$ and $G'$, where $G'$ is the graph associated with the polarization of the ideal $(I(G)^{s+1} : e_1\cdots e_s)$, where $e_1,\ldots e_s$ are edges of $G$. Using these results, we explicitly compute reg$(I(G)^s)$ for several subclasses of bipartite graphs.

Topics: Commutative Algebra, Mathematics

Source: http://arxiv.org/abs/1609.01402

11
11

Jun 29, 2018
06/18

by
A-Ming Liu; Tongsuo Wu

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For each Boolean graph $B_n$, it is proved that both $B_n$ and its complement graph $\overline{B_n}$ are vertex decomposable. It is also proved that $B_n$ is an unmixed graph, thus it is also Cohen-Macaulay.

Topics: Commutative Algebra, Combinatorics, Rings and Algebras, Mathematics

Source: http://arxiv.org/abs/1611.07574

8
8.0

Jun 29, 2018
06/18

by
A-Ming Liu; Tongsuo Wu

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Let $I$ be a graded ideal of $K[x_1,\ldots,x_n]$ generated by homogeneous polynomials of a same degree $d$, and assume that $I$ has linear quotients. In this note, we use Horseshoe Lemma to give a relatively direct inductive construction of a minimal free resolution of $I$, which is called a $d$-linear resolution.

Topics: Commutative Algebra, Mathematics

Source: http://arxiv.org/abs/1610.00055

6
6.0

Jun 30, 2018
06/18

by
A. A. Ambily

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In this paper, we prove the normality of the Roy's elementary orthogonal group (Dickson--Siegel--Eichler--Roy or DSER group) over a commutative ring which was introduced by A. Roy in [MR0231844] under some conditions on the hyperbolic rank. We also establish a stability theorem for $K_1$ of Roy's group. We obtain a decomposition theorem for the elementary orthogonal group which is used to deduce the stability theorem.

Topics: Mathematics, K-Theory and Homology, Commutative Algebra

Source: http://arxiv.org/abs/1401.0822

6
6.0

Jun 30, 2018
06/18

by
A. A. Ambily; Ravi A. Rao

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Let $(Q, q)$ be a quadratic space over a commutative ring $R$ in which $2$ is invertible, and consider the Dickson--Siegel--Eichler--Roy's subgroup $EO_{R}(Q, H(R)^{m})$ of the orthogonal group $O_R(Q \perp H(R)^m)$, with rank $Q= n \geq 1$ and $m\geq 2$. We show that $EO_{R}(Q, H(R)^{m})$ is a normal subgroup of $O_R(Q \perp H(R)^m)$, for all $m\geq 2$. We also prove that the DSER group $EO_{R}(Q, H(P))$ is a normal subgroup of $O_{R}(Q \perp H(P))$, where $Q$ and $H(P)$ are quadratic spaces...

Topics: K-Theory and Homology, Commutative Algebra, Mathematics

Source: http://arxiv.org/abs/1703.04083

6
6.0

Jun 30, 2018
06/18

by
A. A. Ambily; Ravi A. Rao

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We prove that a quadratic $A[T]$-module $Q$ with Witt index ($Q/TQ$)$ \geq d$, where $d$ is the dimension of the equicharacteristic regular local ring $A$, is extended from $A$. This improves a theorem of the second named author who showed it when $A$ is the local ring at a smooth point of an affine variety over an infinite field. To establish our result, we need to establish a Local-Global Principle (of Quillen) for the Dickson--Siegel--Eichler--Roy (DSER) elementary orthogonal transformations.

Topics: Mathematics, K-Theory and Homology, Commutative Algebra

Source: http://arxiv.org/abs/1401.0809

4
4.0

Jun 30, 2018
06/18

by
A. Chirvasitu; S. Paul Smith

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The 4-dimensional Sklyanin algebras are a well-studied 2-parameter family of non-commutative graded algebras, often denoted A(E,tau), that depend on a quartic elliptic curve E in P^3 and a translation automorphism tau of E. They are graded algebras generated by four degree-one elements subject to six quadratic relations and in many important ways they behave like the polynomial ring on four indeterminates apart from the minor difference that they are not commutative. They are elliptic analogues...

Topics: Quantum Algebra, Mathematics

Source: http://arxiv.org/abs/1702.00377

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6.3K

Aug 16, 2013
08/13

by
A. G. Kurosh

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This booklet is a revision of the authorâs lecture to high school students taking part in the Mathematics Olympiad at Moscow State University. It gives a review of the results and methods of the general theory of algebraic equations with due regard for the level of knowledge of its readers. No proofs are included in the text since this would have required copying almost half of a university textbook on higher algebra. Despite such an approach, this booklet does not make for light reading. Even...

Topics: mathematics, algebra, equations, arbitrary degree, mir publishers, little mathematics library

94
94

Feb 26, 2022
02/22

by
A. G. Kúrosch

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El Profesor A.G. Kúrosch hace una exposición magistral de la resolución de ecuaciones, a nivel elemental. Es de carácter explicativo, sin grandes demostraciones, para enmarcarlo a nivel de la Enseñanza Media. Contenido: Prefacio 1. Introducción 2. Números Complejos 3. Extracción de raíces. Ecuaciones cuadráticas 4. Ecuaciones cúbicas 5. Acerca de la resolución de ecuaciones bajo radicales y de la existencia de raices de las ecuaciones 6. Número de...

Topics: Mathematics, Algebra, Lecciones Populares de Matemáticas, Editorial Mir, Moscú, Spanish

0
0.0

Nov 27, 2022
11/22

by
A. G. Kúrosch

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Primera edición 1976 Segunda edición 1983 Traducido del Ruso por el Silvia de Sepulveda Esle librito. ha sido escrito a base de las clases que el autor dictara en la Universidad Estatal Lomonósov de Moscú para Jos participantes de la olimpíada matemátic~, alumnos del noveno y décimo grados. En el mismo se traza, de acuerdo con el nivel de conocimien· tos de un alumno del noveno grado, un resumen de los resultados y métodos de la teorla general de las ecuaciones a lgebraicas. Prácti·...

Topics: Lecciones Populares De Matemáticas, Matemáticas, algebra

163
163

Dec 15, 2020
12/20

by
A. G. Kúrosh

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Clases que el autor dictara para los alumnos participantes de la olimpiada de matemáticas.

Topics: Ecuaciones algebraicas, matemáticas, lecciones populares, algébra

2,474
2.5K

Nov 17, 2021
11/21

by
A. I. Borisenko; I. E. Tarapov

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he present book is a freely revised and restyled version of the third edition of the Russian original (Moscow, 1966). As in other volumes of this series, I have not hesitated to introduce a number of pedagogical and mathematical improvements that occurred to me in the course of doing the translation. 1 have also added a brief Bibliography, confined to books in English dealing with approximately the same topics, at about the same level.

Topics: physics, mathematics, tensors, vectors, analysis, theorems, vector algebra, green's formula,...

571
571

Dec 20, 2019
12/19

by
A. I. Markushevich

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This book has been written mainly for high school students, but it will also be helpful to anyone studying on their own whose mathematical education is confined to high school mathematics. The book is based on a lecture I gave to Moscow schoolchildren of grades 7 and 8 (13 and 14 years old). In preparing the lecture for publication I expanded the material,while at the same time trying not to make the treatment any less accessible. The most substantial addition is Section 13 on the ellipse,...

Topics: mathematics, graphs, equations, curves, algebra, geometry, high school

103
103

Feb 27, 2022
02/22

by
A. I. Markushévich

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El concepto de sucesión recurrente es una amplia generalización del concepto de progresión aritmética o geométrica. También comprende como casos particulares las sucesiones de cuadrados o cubos de los números naturales, las sucesiones de las cifras de la descomposición decimal de los números racionales, las sucesiones de los coeficientes del cociente que se obtiene al dividir dos polinomios cualesquiera escritos en el orden creciente de las potencias de x, etc. En el presente librito...

Topics: Mathematics, Algebra, Lecciones Populares de Matemáticas, Editorial Mir, Moscú, Spanish

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22

Jun 28, 2018
06/18

by
A. Kaygun; S. Sütlü

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We show that if $G$ is a compact Lie group and $\mathfrak{g}$ is its Lie algebra, then there is a map from the Hopf-cyclic cohomology of the quantum enveloping algebra $U_q(\mathfrak{g})$ to the twisted cyclic cohomology of quantum group algebra $\mathcal{O}(G_q)$. We also show that the Schm\"udgen-Wagner index cocycle associated with the volume form of the differential calculus on the standard Podle\'s sphere $\mathcal{O}(S^2_q)$ is in the image of this map.

Topics: Mathematics, Quantum Algebra

Source: http://arxiv.org/abs/1507.07041

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144

Jul 27, 2017
07/17

by
A. Kurosh

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Higher Algebra, MIR

Topic: Algebra

2,009
2.0K

Jun 3, 2021
06/21

by
A. Kurosh

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Higher algebra—the subject of this text—is a far-reaching and natural generalization of the basic school course of elementary algebra. Central to elementary algebra is without doubt the problem of solving equations. The study of equations begins with the very simple case of one equation of the first degree in one unknown. From there on, the development proceeds in two directions: to systems of two and three equations of the first degree in two and, respectively, three unknowns, and to a...

Topics: mathematics, mir books, mir publishers, algebra, linear equations, matrices, polynomials, complex...

1,922
1.9K

Oct 23, 2018
10/18

by
A. Kuroš

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Curso de álgebra superior por A. Kuroš (1968) Traducido al castellano por Emiliano Aparicio Bernardo

Topics: Editorial MIR, álgebra

9
9.0

Jun 29, 2018
06/18

by
A. L. Agore

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We completely describe by generators and relations and classify all Hopf algebras which factorize through the Taft algebra $T_{m^{2}}(q)$ and the group Hopf algebra $K[C_{n}]$: they are $nm^{2}$-dimensional quantum groups $T_{nm^{2}}^ {\omega}(q)$ associated to an $n$-th root of unity $\omega$. Furthermore, using Dirichlet's prime number theorem we are able to count the number of isomorphism types of such Hopf algebras. More precisely, if $d = {\rm gcd}(m,\,\nu(n))$ and...

Topics: Quantum Algebra, Rings and Algebras, Mathematics

Source: http://arxiv.org/abs/1611.05674

7
7.0

Jun 30, 2018
06/18

by
A. L. Agore

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Using Wederburn's main theorem and a result of Gerstenhaber we prove that, over a field of characteristic zero, the maximal dimension of a proper unital subalgebra in the $n \times n$ matrix algebra is $n^2 - n + 1$ and furthermore this upper bound is attained for the so-called parabolic subalgebras. We also investigate the corresponding notion of parabolic coideals for matrix coalgebras and prove that the minimal dimension of a non-zero coideal of the matrix coalgebra ${\mathcal M}^n (k)$ is...

Topics: Mathematics, Quantum Algebra, Rings and Algebras

Source: http://arxiv.org/abs/1403.0773

7
7.0

Jun 30, 2018
06/18

by
A. L. Agore

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We construct the analogue of Takeuchi's free Hopf algebra in the setting of Poisson Hopf algebras. More precisely, we prove that there exists a free Poisson Hopf algebra on any coalgebra or, equivalently that the forgetful functor from the category of Poisson Hopf algebras to the category of coalgebras has a left adjoint. In particular, we also prove that the category of Poisson Hopf algebras is a reflective subcategory of the category of Poisson bialgebras. Along the way, we describe...

Topics: Quantum Algebra, Mathematics, Category Theory, Rings and Algebras

Source: http://arxiv.org/abs/1404.0170

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94

Apr 10, 2022
04/22

by
A. Lentin, J. Rivaud

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La inclusión en los programas de los cursos universitarios iniciales de conceptos de álgebra relativamente modernos, plantea la necesidad urgente de disponer de un texto de introducción que sirva de guía a los alumnos que no tienen otros conocimientos matemáticos que los adquiridos en el bachillerato. Los temas aquí tratados se consideran indispensables para quienes hayan de seguir estudios de física o matemática: conjuntos y funciones; grupos, anillos, cuerpos, números reales y...

Topics: álgebra, matemáticas, modernas

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Jun 28, 2018
06/18

by
A. Levin; M. Olshanetsky; A. Zotov

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We consider Yang-Baxter equations arising from its associative analog and study corresponding exchange relations. They generate finite-dimensional quantum algebras which have form of coupled ${\rm GL}(N)$ Sklyanin elliptic algebras. Then we proceed to a natural generalization of the Baxter-Belavin quantum $R$-matrix to the case ${\rm Mat}(N,\mathbb C)^{\otimes 2}\otimes {\rm Mat}(M,\mathbb C)^{\otimes 2}$. It can be viewed as symmetric form of ${\rm GL}(NM)$ $R$-matrix in the sense that the...

Topics: Quantum Algebra, Mathematical Physics, Mathematics, High Energy Physics - Theory

Source: http://arxiv.org/abs/1507.02617

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7.0

Jun 30, 2018
06/18

by
A. Levin; M. Olshanetsky; A. Zotov

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We describe classical top-like integrable systems arising from the quantum exchange relations and corresponding Sklyanin algebras. The Lax operator is expressed in terms of the quantum non-dynamical $R$-matrix even at the classical level, where the Planck constant plays the role of the relativistic deformation parameter in the sense of Ruijsenaars and Schneider (RS). The integrable systems (relativistic tops) are described as multidimensional Euler tops, and the inertia tensors are written in...

Topics: High Energy Physics - Theory, Nonlinear Sciences, Mathematics, Quantum Algebra, Exactly Solvable...

Source: http://arxiv.org/abs/1405.7523

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5.0

Jun 29, 2018
06/18

by
A. M. Gainutdinov; H. Saleur

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Finite Temperley-Lieb (TL) algebras are diagram-algebra quotients of (the group algebra of) the famous Artin's braid group $B_N$, while the affine TL algebras arise as diagram algebras from a generalized version of the braid group. We study asymptotic `$N\to\infty$' representation theory of these quotients (parametrized by $q\in\mathbb{C}^{\times}$) from a perspective of braided monoidal categories. Using certain idempotent subalgebras in the finite and affine algebras, we construct infinite...

Topics: High Energy Physics - Theory, Mathematics, Category Theory, Quantum Algebra, Representation Theory,...

Source: http://arxiv.org/abs/1606.04530

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8.0

Jun 30, 2018
06/18

by
A. M. Gainutdinov; N. Read; H. Saleur; R. Vasseur

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The periodic sl(2|1) alternating spin chain encodes (some of) the properties of hulls of percolation clusters, and is described in the continuum limit by a logarithmic conformal field theory (LCFT) at central charge c=0. This theory corresponds to the strong coupling regime of a sigma model on the complex projective superspace $\mathbb{CP}^{1|1} = \mathrm{U}(2|1) / (\mathrm{U}(1) \times \mathrm{U}(1|1))$, and the spectrum of critical exponents can be obtained exactly. In this paper we push the...

Topics: High Energy Physics - Theory, Statistical Mechanics, Mathematics, Quantum Algebra, Representation...

Source: http://arxiv.org/abs/1409.0167

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8.0

Jun 28, 2018
06/18

by
A. M. Pavlyuk

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For the one-parameter Alexander (Jones) skein relation we introduce the Alexander (Jones) "bosonic" q-numbers, and for the two-parameter HOMFLY skein relation we propose the HOMFLY "bosonic" (q,p)-numbers ("bosonic" numbers connected with deformed bosonic oscillators). With the help of these deformed "bosonic" numbers, the corresponding skein relations can be reproduced. Analyzing the introduced "bosonic" numbers, we point out two ways of...

Topics: High Energy Physics - Theory, Mathematical Physics, Quantum Algebra, Mathematics

Source: http://arxiv.org/abs/1511.09297

4
4.0

Jun 30, 2018
06/18

by
A. Mahdikhani; P. Sahandi; N. Shirmohammadi

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Our goal is to determine when the trivial extensions of commutative rings by modules are Cohen-Macaulay in the sense of Hamilton and Marley. For this purpose, we provide a generalization of the concept of Cohen-Macaulayness of rings to modules.

Topics: Commutative Algebra, Mathematics

Source: http://arxiv.org/abs/1701.08489

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4.0

Jun 29, 2018
06/18

by
A. Mironov; A. Morozov

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We connect two important conjectures in the theory of knot polynomials. The first one is the property Al_R(q) = Al_{[1]}(q^{|R|}) for all single hook Young diagrams R, which is known to hold for all knots. The second conjecture claims that all the mixing matrices U_{i} in the relation {\cal R}_i = U_i{\cal R}_1U_i^{-1} between the i-th and the first generators {\cal R}_i of the braid group are universally expressible through the eigenvalues of {\cal R}_1. Since the above property of Alexander...

Topics: High Energy Physics - Theory, Geometric Topology, Quantum Algebra, Mathematics

Source: http://arxiv.org/abs/1610.03043

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Jun 27, 2018
06/18

by
A. Mironov; A. Morozov

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Construction of (colored) knot polynomials for double-fat graphs is further generalized to the case when "fingers" and "propagators" are substituting R-matrices in arbitrary closed braids with m-strands. Original version of arXiv:1504.00371 corresponds to the case m=2, and our generalizations sheds additional light on the structure of those mysterious formulas. Explicit expressions are now combined from Racah matrices of the type $R\otimes R\otimes\bar R\longrightarrow \bar...

Topics: Geometric Topology, Quantum Algebra, Mathematics, High Energy Physics - Theory

Source: http://arxiv.org/abs/1506.00339

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10.0

Jun 28, 2018
06/18

by
A. Mironov; A. Morozov

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By now it is well established that the quantum dimensions of descendants of the adjoint representation can be described in a universal form, independent of a particular family of simple Lie algebras. The Rosso-Jones formula then implies a universal description of the adjoint knot polynomials for torus knots, which in particular unifies the HOMFLY (SU_N) and Kauffman (SO_N) polynomials. For E_8 the adjoint representation is also fundamental. We suggest to extend the universality from the...

Topics: Geometric Topology, Quantum Algebra, Representation Theory, Mathematics, High Energy Physics -...

Source: http://arxiv.org/abs/1511.09077

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100

Jun 30, 2018
06/18

by
A. Mironov; A. Morozov; A. Sleptsov

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With the help of the evolution method we calculate all HOMFLY polynomials in all symmetric representations [r] for a huge family of (generalized) pretzel links, which are made from g+1 two strand braids, parallel or antiparallel, and depend on g+1 integer numbers. We demonstrate that they possess a pronounced new structure: are decomposed into a sum of a product of g+1 elementary polynomials, which are obtained from the evolution eigenvalues by rotation with the help of rescaled SU_q(N) Racah...

Topics: High Energy Physics - Theory, Mathematics, Quantum Algebra, Geometric Topology

Source: http://arxiv.org/abs/1412.8432

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Jun 29, 2018
06/18

by
A. Mironov; A. Morozov; An. Morozov; A. Sleptsov

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We construct a general procedure to extract the exclusive Racah matrices S and \bar S from the inclusive 3-strand mixing matrices by the evolution method and apply it to the first simple representations R =[1], [2], [3] and [2,2]. The matrices S and \bar S relate respectively the maps (R\otimes R)\otimes \bar R\longrightarrow R with R\otimes (R \otimes \bar R) \longrightarrow R and (R\otimes \bar R) \otimes R \longrightarrow R with R\otimes (\bar R \otimes R) \longrightarrow R. They are...

Topics: High Energy Physics - Theory, Geometric Topology, Quantum Algebra, Mathematics

Source: http://arxiv.org/abs/1605.04881

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4.0

Jun 29, 2018
06/18

by
A. Mironov; A. Morozov; An. Morozov; A. Sleptsov

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This paper is a new step in the project of systematic description of colored knot polynomials started in arXiv:1506.00339. In this paper, we managed to explicitly find the inclusive Racah matrix, i.e. the whole set of mixing matrices in channels R^3->Q with all possible Q, for R=[3,1]. The calculation is made possible by the use of a newly-developed efficient highest-weight method, still it remains tedious. The result allows one to evaluate and investigate [3,1]-colored polynomials for...

Topics: High Energy Physics - Theory, Geometric Topology, Quantum Algebra, Mathematics

Source: http://arxiv.org/abs/1605.02313

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Jun 28, 2018
06/18

by
A. Mironov; A. Morozov; An. Morozov; A. Sleptsov

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This paper starts a systematic description of colored knot polynomials, beginning from the first non-(anti)symmetric representation R=[2,1]. The project involves several steps: (i) parametrization of big families of knots a la arXiv:1506.00339, (ii) evaluating Racah/mixing matrices for various numbers of strands in various representations a la arXiv:1112.2654, (iii) tabulating and collecting the results at www.knotebook.org. In this paper we discuss only representation R=[2,1] and construct all...

Topics: Geometric Topology, Quantum Algebra, Mathematics, High Energy Physics - Theory

Source: http://arxiv.org/abs/1508.02870

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Jun 29, 2018
06/18

by
A. Mironov; A. Morozov; An. Morozov; A. Sleptsov

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We describe the inclusive Racah matrices for the first non-(anti)symmetric rectangular representation R=[2,2] for quantum groups U_q(sl_N). Most of them have sizes 2, 3, and 4 and are fully described by the eigenvalue hypothesis. Of two 6x6 matrices, one is also described in this way, but the other one corresponds to the case of degenerate eigenvalues and is evaluated by the highest weight method. Together with the much harder calculation for R=[3,1] in arXiv:1605.02313 and with the new method...

Topics: High Energy Physics - Theory, Geometric Topology, Quantum Algebra, Mathematics

Source: http://arxiv.org/abs/1605.03098

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Jun 27, 2018
06/18

by
A. Mironov; A. Morozov; An. Morozov; P. Ramadevi; Vivek Kumar Singh

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Many knots and links in S^3 can be drawn as gluing of three manifolds with one or more four-punctured S^2 boundaries. We call these knot diagrams as double fat graphs whose invariants involve only the knowledge of the fusion and the braiding matrices of four-strand braids. Incorporating the properties of four-point conformal blocks in WZNW models, we conjecture colored HOMFLY polynomials for these double fat graphs where the color can be rectangular or non-rectangular representation. With the...

Topics: High Energy Physics - Theory, Geometric Topology, Mathematics, Quantum Algebra

Source: http://arxiv.org/abs/1504.00371

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109

Jun 29, 2018
06/18

by
A. Mironov; A. Morozov; An. Morozov; P. Ramadevi; Vivek Kumar Singh; A. Sleptsov

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Arborescent knots are the ones which can be represented in terms of double fat graphs or equivalently as tree Feynman diagrams. This is the class of knots for which the present knowledge is enough for lifting topological description to the level of effective analytical formulas. The paper describes the origin and structure of the new tables of colored knot polynomials, which will be posted at the dedicated site. Even if formal expressions are known in terms of modular transformation matrices,...

Topics: High Energy Physics - Theory, Representation Theory, Geometric Topology, Quantum Algebra,...

Source: http://arxiv.org/abs/1601.04199

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83

Jun 28, 2018
06/18

by
A. Mironov; R. Mkrtchyan; A. Morozov

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We present a universal knot polynomials for 2- and 3-strand torus knots in adjoint representation, by universalization of appropriate Rosso-Jones formula. According to universality, these polynomials coincide with adjoined colored HOMFLY and Kauffman polynomials at SL and SO/Sp lines on Vogel's plane, and give their exceptional group's counterparts on exceptional line. We demonstrate that [m,n]=[n,m] topological invariance, when applicable, take place on the entire Vogel's plane. We also...

Topics: Geometric Topology, Quantum Algebra, Mathematics, High Energy Physics - Theory

Source: http://arxiv.org/abs/1510.05884

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7.0

Jun 29, 2018
06/18

by
A. Morozov

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Factorization of the differential expansion coefficients for HOMFLY-PT polynomials of double braids, discovered in arXiv:1606.06015 in the case of rectangular representations $R$, is extended to the first non-rectangular representations $R=[2,1]$ and $R=[3,1]$. This increases chances that such factorization will take place for generic $R$, thus fixing the shape of the DE. We illustrate the power of the method by conjecturing the DE-induced expression for double-braid polynomials for all...

Topics: High Energy Physics - Theory, Geometric Topology, Mathematical Physics, Quantum Algebra, Mathematics

Source: http://arxiv.org/abs/1612.00422

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Jun 27, 2018
06/18

by
A. N. Sergeev; A. P. Veselov

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We study the orbits and polynomial invariants of certain affine action of the super Weyl groupoid of Lie superalgebra $\mathfrak {gl}(n,m)$, depending on a parameter. We show that for generic values of the parameter all the orbits are finite and separated by certain explicitly given invariants. We also describe explicitly the special set of parameters, for which the algebra of invariants is not finitely generated and does not separate the orbits, some of which are infinite.

Topics: Commutative Algebra, Mathematics, Representation Theory

Source: http://arxiv.org/abs/1504.08310

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5.0

Jun 30, 2018
06/18

by
A. Nyman

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Let $k$ be a field. We describe necessary and sufficient conditions for a $k$-linear abelian category to be a noncommutative $\mathbb{P}^{1}$-bundle over a pair of division rings over $k$. As an application, we prove that $\mathbb{P}^{1}_{n}$, Piontkovski's $n$th noncommutative projective line, is the noncommutative projectivization of an $n$-dimensional vector space.

Topics: Quantum Algebra, Rings and Algebras, Algebraic Geometry, Mathematics

Source: http://arxiv.org/abs/1704.04544

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Jun 27, 2018
06/18

by
A. Nyman

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Let k be a field. We show that all homogeneous noncommutative curves of genus zero over k are noncommutative P^1-bundles over a (possibly) noncommutative base. Using this result, we compute complete isomorphism invariants of homogeneous noncommutative curves of genus zero, allowing us to generalize a theorem of Witt.

Topics: Algebraic Geometry, Mathematics, Quantum Algebra

Source: http://arxiv.org/abs/1503.04341