Journal of Lie Theory 31 (2021), No. 1, 149--168
Copyright Heldermann Verlag 2021
On Hom-Pre-Lie Bialgebras
Shanshan Liu
Dept. of Mathematics, Jilin University, Changchun 130012, P. R. China
shanshan18@mails.jlu.edu.cn
Abdenacer Makhlouf
IRIMAS -- Dép. de Mathématiques, University of Haute Alsace, Mulhouse, France
abdenacer.makhlouf@uha.fr
Lina Song
Dept. of Mathematics, Jilin University, Changchun 130012, P. R. China
songln@jlu.edu.cn
We introduce Hom-pre-Lie bialgebras 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 Hom-O-operators on Hom-pre-Lie algebras and Hom-L-dendriform algebras, by which we construct Hom-s-matrices.
Keywords: Hom-pre-Lie algebra, Manin triple, Hom-pre-Lie bialgebra, Hom-s-equation.
MSC: 16T25, 17B62, 17B99.
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