Yang-Baxter equations and relative Rota-Baxter operators for left-Alia algebras associated to invariant theory
Rings and Algebras
2024-06-28 v1
Abstract
Left-Alia algebras are a class of algebras with symmetric Jacobi identities. They contain several typical types of algebras as subclasses, and are closely related to the invariant theory. In this paper, we study the construction theory of left-Alia bialgebras. We introduce the notion of the left-Alia Yang-Baxter equation. We show that an antisymmetric solution of the left-Alia Yang-Baxter equation gives rise to a left-Alia bialgebra that we call triangular. The notions of relative Rota-Baxter operators of left-Alia algebras and pre-left-Alia algebras are introduced to provide antisymmetric solutions of the left-Alia Yang-Baxter equation.
Cite
@article{arxiv.2406.18843,
title = {Yang-Baxter equations and relative Rota-Baxter operators for left-Alia algebras associated to invariant theory},
author = {Kang Chuangchuang and Liu Guilai and Shizhuo Yu},
journal= {arXiv preprint arXiv:2406.18843},
year = {2024}
}
Comments
arXiv admin note: text overlap with arXiv:2403.05339