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On Hom-pre-Lie bialgebras

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arxiv 1912.13418 v1 pith:OTSENXLJ submitted 2019-12-27 math.RA

Shanshan Liu , Abdenacer Makhlouf , Lina Song This is my paper
classification math.RA
keywords hom-pre-liealgebrasbialgebrascohomologyconstructintroducenotiontheory
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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.

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