Abstract
We present a class of Poisson structures on trivial extension algebras which generalizes 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 presented. Examples coming from Poisson modules and Poisson submanifolds are given.
Original language | English |
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Article number | 54 |
Journal | Bulletin of the Brazilian Mathematical Society |
Volume | 54 |
Issue number | 4 |
DOIs | |
State | Published - Dec 2023 |
Bibliographical note
Publisher Copyright:© 2023, The Author(s), under exclusive licence to Brazilian Mathematical Society.
Keywords
- Contravariant derivative
- Lie algebroid
- Poisson algebra
- Poisson cohomology
- Poisson module
- Poisson submanifold
- Trivial extension algebra