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arXiv · 2109.03460

Poisson Structures on Trivial Extension Algebras

D. García-Beltrán·J. C. Ruíz-Pantaleón·Yu. Vorobiev
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Abstract

We present a class of Poisson structures on trivial extension algebras which generalize some known structures induced by Poisson modules. We show that there exists a one-to-one correspondence between such a class of Poisson structures and some data involving (not necessarily flat) contravariant derivatives, and then we give a formulation of this result in terms of Lie algebroids. Some properties of the first Poisson cohomology are also presented. Examples coming from Poisson modules and Poisson submanifolds are given.

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BibTeXRIS

D. García-Beltrán, J. C. Ruíz-Pantaleón, Yu. Vorobiev. 2021-09-08. Poisson Structures on Trivial Extension Algebras. https://arxiv.org/abs/2109.03460

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