On Hom-pre-Lie bialgebras
Rings and Algebras
2020-01-01 v1
Abstract
In this paper we introduce the notion of Hom-pre-Lie bialgebra in the general framework of the cohomology theory for Hom-Lie algebras. We show that Hom-pre-Lie bialgebras, standard Manin triples for Hom-pre-Lie algebras and certain matched pairs of Hom-pre-Lie algebras are equivalent. Due to the usage of the cohomology theory, it makes us successfully study the coboundary Hom-pre-Lie bialgebras. The notion of Hom-s-matrix is introduced, by which we can construct Hom-pre-Lie bialgebras naturally. Finally we introduce the notions of Hom-O-operators on Hom-pre-Lie algebras and Hom-L-dendriform algebras, by which we construct Hom-s-matrices.
Keywords
Cite
@article{arxiv.1912.13418,
title = {On Hom-pre-Lie bialgebras},
author = {Shanshan Liu and Abdenacer Makhlouf and Lina Song},
journal= {arXiv preprint arXiv:1912.13418},
year = {2020}
}