The Hom–Yang–Baxter equation and Hom–Lie algebras

Source abstract

Motivated by recent work on Hom–Lie algebras, a twisted version of the Yang–Baxter equation, called the Hom–Yang–Baxter equation (HYBE), was introduced by Yau [J. Phys. A 42, 165202 (2009)]. In this paper, several more classes of solutions of the HYBE are constructed. Some of the solutions of the HYBE are closely related to the quantum enveloping algebra of \documentclass[12pt]{minimal}\begin{document}$\mathfrak {sl}(2)$\end{document}sl(2), the Jones–Conway polynomial, and Yetter-Drinfel'd modules. Under some invertibility conditions, we construct a new infinite sequence of solutions of the HYBE from a given one.