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Representations and cohomologies of Hom-pre-Lie algebras

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arxiv 1902.07360 v1 pith:OFYOOPVX submitted 2019-02-20 math.RA

Shanshan Liu , Lina Song , Rong Tang This is my paper
classification math.RA
keywords hom-pre-liealgebrasalgebracohomologynotionrepresentationsdeformationshessian
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abstract

In this paper, first we study dual representations and tensor representations of Hom-pre-Lie algebras. Then we develop the cohomology theory of Hom-pre-Lie algebras in term of the cohomology theory of Hom-Lie algebras. As applications, we study linear deformations of Hom-pre-Lie algebras, which are characterized by the second cohomology groups of Hom-pre-Lie algebras with the coefficients in the regular representation. The notion of a Nijenhuis operator on a Hom-pre-Lie algebra is introduced which can generate trivial linear deformations of a Hom-pre-Lie algebra. Finally, we introduce the notion of a Hessian structure on a Hom-pre- Lie algebra, which is a symmetric nondegenerate 2-cocycle with the coefficient in the trivial representation. We also introduce the notion of an $\huaO$-operator on a Hom-pre-Lie algebra, by which we give an equivalent characterization of a Hessian structure.

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Cited by 1 Pith paper

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  1. Cohomology and linear deformation of BiHom-left-symmetric algebras

    math.RA 2019-07 unverdicted novelty 5.0 of 10

    Develops cohomology for BiHom-left-symmetric algebras and characterizes their linear deformations by the second cohomology group with adjoint coefficients.

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