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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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Central Endomorphisms of Groups and Radical Rings [PDF]
Advances in Group Theory and Applications, 2023 An endomorphism γ of a group G is called a central endomorphism if x^-1 xγ lies into the centre Z(G) of G for each element x of G. It is easy to show that all non-zero central endomorphisms of G are automorphisms if and only if the ring R = Hom(G, Z(G ...
Alessio Russo, Mario Viscusi
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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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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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, 2006 Preprint of an Encyclopedia article (Encyclopedia of Mathematical Physics, eds. J.-P. Françoise, G.L. Naber and Tsou S.T., Oxford: Elsevier, 2006 (ISBN 978-0-1251-2666-3), volume 5, pages 465-473) extended with an appendix on relations of electric networks and solvable models. We welcome comments, especially on the added appendix. Please, note that the
Perk, Jacques H. H., Au-Yang, Helen
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Quantum groups, Yang–Baxter maps and quasi-determinants
Nuclear Physics B, 2018 For any quasi-triangular Hopf algebra, there exists the universal R-matrix, which satisfies the Yang–Baxter equation. It is known that the adjoint action of the universal R-matrix on the elements of the tensor square of the algebra constitutes a quantum ...
Zengo Tsuboi
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Affine actions and the Yang–Baxter equation [PDF]
Advances in Operator Theory, 2018 22 pages ...
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On the parametrization of solutions of the Yang--Baxter equations
Open Communications in Nonlinear Mathematical Physics, 2022 We study all five-, six-, and one eight-vertex type two-state solutions of the Yang-Baxter equations in the form $A_{12} B_{13} C_{23} = C_{23} B_{13} A_{12}$, and analyze the interplay of the `gauge' and `inversion' symmetries of these solution. Starting with algebraic solutions, whose parameters have no specific interpretation, and then using these ...
J. Hietarinta, C. Viallet
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Tri-vector deformations on compact isometries
European Physical Journal C: Particles and Fields, 2023 Classical Yang–Baxter equation governing bi-vector deformations of 10d supergravity is known to have no solutions along non-abelian compact isometries.
Edvard T. Musaev, Timophey Petrov
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A Yang–Baxter equation for metaplectic ice [PDF]
Communications in Number Theory and Physics, 2019 We will give new applications of quantum groups to the study of spherical Whittaker functions on the metaplectic $n$-fold cover of $GL(r,F)$, where $F$ is a nonarchimedean local field. Earlier Brubaker, Bump, Friedberg, Chinta and Gunnells had shown that these Whittaker functions can be identified with the partition functions of statistical mechanical ...
Brubaker, Ben +3 more
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