On Hom-pre-Poisson algebras
Rings and Algebras
2021-09-23 v1 Mathematical Physics
math.MP
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.
Keywords
Cite
@article{arxiv.2109.10544,
title = {On Hom-pre-Poisson algebras},
author = {Shanshan Liu and Abdenacer Makhlouf and Lina Song},
journal= {arXiv preprint arXiv:2109.10544},
year = {2021}
}