Poisson Structures on Trivial Extension Algebras
Rings and Algebras
2023-08-30 v3 Commutative Algebra
Differential Geometry
Symplectic Geometry
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.
Cite
@article{arxiv.2109.03460,
title = {Poisson Structures on Trivial Extension Algebras},
author = {D. García-Beltrán and J. C. Ruíz-Pantaleón and Yu. Vorobiev},
journal= {arXiv preprint arXiv:2109.03460},
year = {2023}
}
Comments
31 pages