Set-theoretical solutions to the Hom-Yang-Baxter equation and Hom-cycle sets

2022/12/01 by Kaiqiang Zhang, Zhang, Kaiqiang, Xiankun Du +1
Mathematics · #16T25 #20N02 #20N05 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Rings and Algebras (math.RA) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2212.00274

openalex publication_date 2022/12/01 · openalex created_date 2022/12/13 · openalex updated_date 2026/07/28

Abstract

Set-theoretic solutions to the Yang-Baxter equation have been studied extensively by means of related algebraic systems such as cycle sets and braces, dynamical versions of which have also been developed. No work focuses on set-theoretic solutions to the Hom-Yang-Baxter equation (HYBE for short). This paper investigates set-theoretic solutions to HYBE and associated algebraic system, called Hom-cycle sets. We characterize left non-degenerate involutive set-theoretic solutions to HYBE and Hom-cycle sets, and establish their relations. We discuss connections among Hom-cycle sets, cycle sets, left non-degenerate involutive set-theoretic solutions to HYBE and the Yang-Baxter equation.

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