English

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}
}