2025/02/07 by Benali, Karima
#16T10 #16T25 #17B61 #17B62 #17B63 #FOS: Mathematics #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.2504.03645
In this paper, we present and explore several key concepts within the framework of Hom-Poisson algebras. Specifically, we introduce the notions of admissible Hom-Poisson algebras, along with the related ideas of matched pairs and Manin triples for such algebras. We then define the concept of a purely admissible Hom-Poisson bialgebra, placing particular emphasis on its compatibility with the Manin triple structure associated with a nondegenerate symmetric bilinear form. This compatibility is crucial for understanding the structural interplay between these algebraic objects. Additionally, we investigate the notion of Hom- \mathcal O-operators acting on admissible Hom-Poisson algebras. We analyze their properties and establish a connection with admissible Hom-pre-Poisson algebras, shedding light on the relationship between these two structures.