On commuting solutions of the Yang–Baxter-like matrix equation
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DOI: 10.1016/j.jmaa.2018.02.030
Abstract: Abstract Let A be an arbitrary square matrix and its Jordan canonical form is P − 1 A P = J = diag ( J 1 ( λ 1 ) , ⋯ , J q… read more here.
Keywords: baxter like; solutions yang; matrix equation; yang baxter ... See more keywords
The matched product of set-theoretical solutions of the Yang-Baxter equation
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DOI: 10.1016/j.jpaa.2019.07.012
Abstract: Abstract In this work, we develop a novel construction technique for set-theoretical solutions of the Yang-Baxter equation. Our technique, named the matched product, is an innovative tool to construct new classes of involutive solutions as… read more here.
Keywords: product; solutions yang; yang baxter; set theoretical ... See more keywords
On the indecomposable involutive set-theoretic solutions of the Yang-Baxter equation of prime-power size
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DOI: 10.1080/00927872.2019.1710163
Abstract: Abstract We develop a method to construct all the indecomposable involutive non-degenerate set-theoretic solutions of the Yang-Baxter equation with a prime-power number of elements and cyclic permutation group. Moreover, we give a complete classification of… read more here.
Keywords: solutions yang; baxter equation; theoretic solutions; indecomposable involutive ... See more keywords
Indecomposable solutions of the Yang-Baxter equation with permutation group of sizes pq and p2q
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DOI: 10.1080/00927872.2023.2200827
Abstract: In this paper we study the problem of classification of indecomposable solutions of the Yang-Baxter equation. Using a scheme proposed by Bachiller, Ced\'o, and Jespers, and recent advances in the classification of braces we classify… read more here.
Keywords: solutions yang; indecomposable solutions; baxter equation; permutation ... See more keywords
Decomposition Theorems for Involutive Solutions to the Yang–Baxter Equation
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DOI: 10.1093/imrn/rnab232
Abstract: Motivated by the proof of Rump of a conjecture of Gateva–Ivanova on the decomposability of square-free solutions to the Yang–Baxter equation, we present several other decomposability theorems based on the cycle structure of a certain… read more here.
Keywords: decomposition theorems; solutions yang; baxter equation; yang baxter ... See more keywords
Classification of indecomposable involutive set-theoretic solutions to the Yang–Baxter equation
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DOI: 10.1515/forum-2019-0274
Abstract: Abstract Using the theory of cycle sets and braces, non-degenerate indecomposable involutive set-theoretic solutions to the Yang–Baxter equation are classified in terms of their universal coverings and their fundamental group. The universal coverings are characterized… read more here.
Keywords: solutions yang; involutive set; indecomposable involutive; theoretic solutions ... See more keywords
Set-theoretic solutions to the Yang–Baxter equation and generalized semi-braces
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DOI: 10.1515/forum-2020-0082
Abstract: Abstract This paper aims to introduce a construction technique of set-theoretic solutions of the Yang–Baxter equation, called strong semilattice of solutions. This technique, inspired by the strong semilattice of semigroups, allows one to obtain new… read more here.
Keywords: solutions yang; semi braces; baxter equation; theoretic solutions ... See more keywords
Finding Solutions to the Yang-Baxter-like Matrix Equation for Diagonalizable Coefficient Matrix
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DOI: 10.3390/sym14081577
Abstract: Let A be a diagonalizable complex matrix. In this paper, we discuss finding solutions to the Yang–Baxter-like matrix equation AXA=XAX. We then present a concrete example to illustrate the validity of the results obtained. read more here.
Keywords: like matrix; solutions yang; baxter like; matrix equation ... See more keywords
Uniconnected solutions to the Yang–Baxter equation arising from self-maps of groups
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DOI: 10.4153/s0008439521000230
Abstract: Abstract Set-theoretic solutions to the Yang–Baxter equation can be classified by their universal coverings and their fundamental groupoids. Extending previous results, universal coverings of irreducible involutive solutions are classified in the degenerate case. These solutions… read more here.
Keywords: baxter equation; equation arising; solutions yang; yang baxter ... See more keywords