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arXiv · 2109.10544

On Hom-pre-Poisson algebras

Shanshan Liu·Abdenacer Makhlouf·Lina Song
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Abstract

In this paper, first we discuss Hom-pre-Poisson algebras and their relationships with Hom-Poisson algebra. Then we introduce the notion of a Hom-pre-Gerstenhaber algebra and show that a Hom-pre-Gerstenhaber algebra gives rise to a Hom-Gerstenhaber algebra. Moreover, we consider Hom-dendriform formal deformations of Hom-zinbiel algebras and show that Hom-pre-Poisson algebras are the corresponding semi-classical limits. Furthermore, we consider Hom-O-operators on Hom-Poisson algebras and study their relationships with Hom-pre-Poisson algebras. Finally, we define the notion of dual-Hom-pre-Poisson algebra and show that a Hom-average-operator on a Hom-Poisson algebra naturally gives rise to a dual-Hom-pre-Poisson algebra.

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Shanshan Liu, Abdenacer Makhlouf, Lina Song. 2021-09-22. On Hom-pre-Poisson algebras. https://arxiv.org/abs/2109.10544

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