An associative analogy of Lie H-pseudobialgebra
Rings and Algebras
2020-07-16 v1 Mathematical Physics
math.MP
Abstract
The purpose of this paper is to study infinitesimal H-pseudobialgebra, which is an associative analogy of Lie H-pseudobialgebra. We first define the infinitesimal H-pseudobialgebra and investigate some properties of this new algebraic structure. Then we consider the coboundary infinitesimal H-pseudobialgebra, which is the subclass of infinitesimal H-pseudobialgebra and we obtain the associative Yang-Baxter equation over an associative H-pseudoalgebra. Finally, we found the connection between the (coboundary) infinitesimal H-pseudobialgebra and the (coboundary) Lie H-pseudobialgebra. Meanwhile, the relationship between the associative Yang-Baxter equation and the classical Yang-Baxter equation (over an H-pseudoalgebra) is established.
Keywords
Cite
@article{arxiv.2007.07251,
title = {An associative analogy of Lie H-pseudobialgebra},
author = {Linlin Liu and Zhitao Guo},
journal= {arXiv preprint arXiv:2007.07251},
year = {2020}
}