Results 21 to 30 of about 43,972 (190)
Mathematics, 2021 Every set with a binary operation satisfying a true statement of propositional logic corresponds to a solution of the quantum Yang-Baxter equation. Quantum B-algebras and L-algebras are closely related to Yang-Baxter equation theory.
Aiping Gan, Aziz Muzammal, Yichuan Yang
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Solutions of the quantum dynamical Yang-Baxter equation and dynamical quantum groups [PDF]
, 1997 The quantum dynamical Yang-Baxter (QDYB) equation is a useful generalization of the quantum Yang-Baxter (QYB) equation introduced by Gervais, Neveu, and Felder.
Etingof, Pavel, Varchenko, Alexander
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Mathematics and Poetry · Yang–Baxter Equations, Boolean Algebras, and BCK-Algebras
Sci, 2022 The current paper explores the potential of the areas between mathematics and poetry. We will first recall some definitions and results that are needed to construct solutions of the Yang–Baxter equation.
Tugce Kalkan +4 more
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Yang-Baxter maps and integrable dynamics [PDF]
, 2002 The hierarchy of commuting maps related to a set-theoretical solution of the quantum Yang-Baxter equation (Yang-Baxter map) is introduced. They can be considered as dynamical analogues of the monodromy and/or transfer-matrices.
A.P. Veselov +30 more
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Braces and the Yang–Baxter Equation [PDF]
Communications in Mathematical Physics, 2014 Several aspects of relations between braces and non-degenerate involutive set-theoretic solutions of the Yang-Baxter equation are discussed and many consequences are derived. In particular, for each positive integer $n$ a finite square-free multipermutation solution of the Yang-Baxter equation with multipermutation level $n$ and an abelian involutive ...
Jespers, Eric, Cedo, F., Okninski, J.
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Problems on Skew Left Braces [PDF]
Advances in Group Theory and Applications, 2019 Braces were introduced by Rump as a generalization of Jacobson radical rings. It turns out that braces allow us to use ring-theoretic and group-theoretic methods for studying involutive solutions to the Yang–Baxter equation.
Leandro Vendramin
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On Solutions to the Set-Theoretical Yang-Baxter Equation in Wajsberg-Algebras
Axioms, 2018 In this work, we introduce Wajsberg algebras which are equivalent structures to MV-algebras in their implicational version, and then we define new notions and give new solutions to the set-theoretical Yang-Baxter equation by using Wajsberg algebras.
Tahsin Oner, Tugce Katican
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All Solutions of the Yang–Baxter-Like Matrix Equation for Nilpotent Matrices of Index Two
Complexity, 2020 Let A be a nilpotent matrix of index two, and consider the Yang–Baxter-like matrix equation AXA=XAX. We first obtain a system of matrix equations of smaller sizes to find all the solutions of the original matrix equation.
Duanmei Zhou, Jiawen Ding
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Representations of the quantum doubles of finite group algebras and solutions of the Yang--Baxter equation [PDF]
, 2005 Quantum doubles of finite group algebras form a class of quasi-triangular Hopf algebras which algebraically solve the Yang--Baxter equation. Each representation of the quantum double then gives a matrix solution of the Yang--Baxter equation.
Dancer, K. A., Isaac, P. S., Links, J.
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Multipermutation Solutions of the Yang–Baxter Equation [PDF]
Communications in Mathematical Physics, 2011 Set-theoretic solutions of the Yang--Baxter equation form a meeting-ground of mathematical physics, algebra and combinatorics. Such a solution consists of a set $X$ and a function r:X x X --> X x X which satisfies the braid relation. We examine solutions here mainly from the point of view of finite permutation groups: a solution gives rise to a map ...
Gateva-Ivanova, Tatiana, Cameron, Peter
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