Results 31 to 40 of about 44,436 (212)
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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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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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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A family of solutions of the Yang–Baxter equation
Journal of Algebra, 2014 11 ...
Bachiller, David, Cedó, Ferran
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The Yang–Baxter equations and differential identities [PDF]
Journal of Mathematical Physics, 1990 The solution of the Yang–Baxter equation for integrable systems is shown to be equivalent to the existence of a differential identity. Quantum integration formulas for the calculation of commutators of monodromy matrices are given. Based on the integration formulas and the systematic use of differential identities, the Yang–Baxter equations for the ...
Pu, Fu-Cho, Sattinger, D. H.
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Left braces and the quantum Yang-Baxter equation [PDF]
, 2019 [EN] Braces were introduced by Rump in 2007 as a useful tool in the study of the set-theoretic solutions of the Yang¿Baxter equation. In fact, several aspects of the theory of finite left braces and their applications in the context of the Yang¿Baxter ...
BALLESTER BOLINCHES, ADOLFO +4 more
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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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Yang-Baxter deformations of Minkowski spacetime [PDF]
, 2015 We study Yang-Baxter deformations of 4D Minkowski spacetime. The Yang-Baxter sigma model description was originally developed for principal chiral models based on a modified classical Yang-Baxter equation.
Jun-ichi Sakamoto +9 more
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