On Hom-pre-Poisson algebras

TL;DR

This paper explores the structure and relationships of Hom-pre-Poisson algebras, introduces Hom-pre-Gerstenhaber algebras, and studies their deformations and operators, advancing the understanding of Hom-algebraic structures.

Contribution

It introduces Hom-pre-Gerstenhaber algebras, links Hom-pre-Poisson and Hom-Poisson algebras, and studies deformations and operators, providing new insights into Hom-algebraic frameworks.

Findings

Hom-pre-Poisson algebras relate to Hom-Poisson algebras.

Hom-pre-Gerstenhaber algebras induce Hom-Gerstenhaber algebras.

Hom-dendriform deformations lead to Hom-pre-Poisson algebras.

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.