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arXiv · 2106.03277

Transposed Hom-Poisson and Hom-pre-Lie Poisson algebras and bialgebras

Ismail Laraiedh·Sergei Silvestrov
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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.

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Ismail Laraiedh, Sergei Silvestrov. 2021-06-06. Transposed Hom-Poisson and Hom-pre-Lie Poisson algebras and bialgebras. https://arxiv.org/abs/2106.03277

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