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Transposed Hom-Poisson and Hom-pre-Lie Poisson algebras and bialgebras (2106.03277v1)
Published 6 Jun 2021 in math.RA and math.QA
Abstract: The notions of transposed Hom-Poisson and Hom-pre-Lie Poisson algebras are introduced. Their bimodules and matched pairs are defined and the relevant properties and theorems are given. The notion of Manin triple of transposed Hom-Poisson algebras is introduced, and its equivalence to the transposed Hom-Poisson bialgebras is investigated. The notion of $\mathcal{O}$-operator is exploited to illustrate the relations existing between transposed Hom-Poisson and Hom-pre-Lie Poisson algebras.