An associative analogy of Lie H-pseudobialgebra

2020/07/14 by Liu, Linlin, Guo, Zhitao
#FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2007.07251

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.

Related

• Infinitesimal Hom-bialgebras and Hom-Lie bialgebras
• On pseudo-bialgebras
• Mock-Lie bialgebras and mock-Lie analogue of the classical Yang-Baxter equation
• The classical Hom-Yang-Baxter equation and Hom-Lie bialgebras
• Cohomology of associative H-pseudoalgebras