Hom-Yang-Baxter equations and Hom-Yang-Baxter systems
Shengxiang Wang, Xiaohui Zhang, Shuangjian Guo
TL;DR
This paper introduces new solutions to the Hom-Yang-Baxter equation derived from various Hom-algebraic structures, proves their self-inverse property, and defines Hom-Yang-Baxter systems with two types of solutions.
Contribution
It presents novel solutions to the Hom-Yang-Baxter equation from Hom-algebras, Hom-coalgebras, and Hom-Lie algebras, and introduces the concept of Hom-Yang-Baxter systems.
Findings
Solutions are self-inverse
New Hom-Yang-Baxter systems are constructed
Examples illustrate the theoretical results
Abstract
In this paper, we mainly present some new solutions of the Hom-Yang-Baxter equation from Hom-algebras, Hom-coalgebras and Hom-Lie algebras, respectively. Also, we prove that these solutions are all self-inverse and give some examples. Finally, we introduce the notion of Hom-Yang-Baxter systems and obtain two kinds of Hom-Yang-Baxter systems.
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Finite Group Theory Research