THE CLASSICAL HOM-YANG-BAXTER EQUATION AND HOM-LIE BIALGEBRAS

Year 2015, Volume: 17 Issue: 17, 11 - 45, 01.06.2015

Donald Yau

https://doi.org/10.24330/ieja.266210

Cited By: 21

Abstract

Motivated by recent work on Hom-Lie algebras and the HomYang-Baxter
equation, we introduce a twisted generalization of the classical
Yang-Baxter equation (CYBE), called the classical Hom-Yang-Baxter equation
(CHYBE). We show how an arbitrary solution of the CYBE induces
multiple infinite families of solutions of the CHYBE. We also introduce the
closely related structure of Hom-Lie bialgebras, which generalize Drinfel’d’s
Lie bialgebras. In particular, we study the questions of duality and cobracket
perturbation and the sub-classes of coboundary and quasi-triangular Hom-Lie
bialgebras.

Keywords

The classical Hom-Yang-Baxter equation, Hom-Lie bialgebra