2021/09/22 by Shanshan Liu, Liu, Shanshan, Abdenacer Makhlouf +3
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.2109.10544
openalex publication_date 2021/09/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.