Multipermutation solutions of the Yang–Baxter equation
, 2012 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 which satisfies the braid relation.We examine solutions ...
Gateva-Ivanova, Tatiana +1 more
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QR-type factorization, the Yang-Baxter equation, and an eigenvalue problem of control theory
, 1989 It is shown that every solution to the Yang-Baxter equation corresponds with the O̧R-type algorithm. The structure of solutions of the Yang-Baxter equation is described and examples relevant to the algebraic Riccati equation are ...
Faibusovich, L.E.
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Semi-braces and the Yang-Baxter equation
, 2017 In this paper we obtain new solutions of the Yang-Baxter equation that are left non-degenerate throught left semi-braces, a generalization of braces introduced by Rump.
Ilaria Colazzo +5 more
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ℤ3 parafermionic chain emerging from Yang-Baxter equation. [PDF]
Sci Rep, 2016 Yu LW, Ge ML.
europepmc +1 more source
Algebraic Structures Related to The Dynamical Yang-Baxter Equation
, 2023 A solution to the set-theoretic Yang-Baxter Equation (YBE) is a braided set. Analogously, a solution to the quiver-theoretic Dynamical Yang-Baxter Equation (DYBE) will be a braided quiver.
FERRI, DAVIDE
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More about the doubling degeneracy operators associated with Majorana fermions and Yang-Baxter equation. [PDF]
Sci Rep, 2015 Yu LW, Ge ML.
europepmc +1 more source
Groups and set theoretic solutions of the Yang-Baxter equation
, 2011 We discuss some recent results on the link between group theory and set theoretic involutive non-degenerate solutions of the Yang-Baxter equation.
Jespers, Eric
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Post-Hopf algebras, relative Rota-Baxter operators and solutions of the Yang-Baxter equation
, 2022 In this paper, first we introduce the notion of a post-Hopf algebra, which gives rise to a post-Lie algebra on the space of primitive elements and there is naturally a post-Hopf algebra structure on the universal enveloping algebra of a post-Lie algebra.
Li, Yunnan, Sheng, Yunhe, Tang, Rong
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Parameter-dependent associative Yang-Baxter equation and Poisson brackets
, 2014 We discuss associative analogues of classical Yang-Baxter equation meromorphically dependent on parameters. We discover that such equations enter in a description of a general class of parameter-dependent Poisson structures and double Lie and Poisson ...
V. Roubtsov, A. Odesskii, V. Sokolov
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Spectral-parameter dependent Yang-Baxter operators and Yang-Baxter systems from algebra structures
For any algebra, two families of colored Yang-Baxter operators are constructed, thus producing solutions to the two-parameter quantum Yang-Baxter equation. An open problem about a system of functional equations is stated.
Parashar, Deepak, Nichita, Florin F.
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