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- W2916856260 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." @default.
- W2916856260 created "2019-03-02" @default.
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- W2916856260 date "2019-02-20" @default.
- W2916856260 modified "2023-09-23" @default.
- W2916856260 title "Representations and cohomologies of Hom-pre-Lie algebras" @default.
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