Local cocycle 3-Hom-Lie Bialgebras and 3-Lie Classical Hom-Yang-Baxter Equation

TL;DR

This paper introduces local cocycle 3-Hom-Lie bialgebras and explores a twisted 3-ary Yang-Baxter equation, establishing a link between solutions of this equation and coboundary structures in these bialgebras.

Contribution

It defines 3-Hom-Lie bialgebras with local cocycle conditions and introduces the 3-Lie classical Hom-Yang-Baxter Equation, connecting solutions to coboundary bialgebra structures.

Findings

Defined 3-Hom-Lie bialgebras with local cocycle conditions

Introduced the 3-Lie classical Hom-Yang-Baxter Equation

Proved solutions induce coboundary local cocycle 3-Hom-Lie bialgebras

Abstract

In this paper, we introduce 3-Hom-Lie bialgebras whose compatibility conditions between the multiplication and comultiplication are given by local cocycle conditions. We study a twisted 3-ary version of the Yang-Baxter Equation, called the 3-Lie classical HomYang-Baxter Equation (3-Lie CHYBE), which is a general form of 3-Lie classical YangBaxter Equation studied in [2] and prove that the bialgebras induced by the solutions of 3-Lie CHYBE induce the coboundary local cocycle 3-Hom-Lie bialgebras.