Poisson Structures on Trivial Extension Algebras

D. García-Beltrán; J. C. Ruíz-Pantaleón; Yu Vorobiev

doi:10.1007/s00574-023-00366-4

Poisson Structures on Trivial Extension Algebras

D. García-Beltrán^*, J. C. Ruíz-Pantaleón, Yu Vorobiev

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

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
Article number	54
Journal	Bulletin of the Brazilian Mathematical Society
Volume	54
Issue number	4
DOIs	https://doi.org/10.1007/s00574-023-00366-4
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

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10.1007/s00574-023-00366-4

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title = "Poisson Structures on Trivial Extension Algebras",

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.",

keywords = "Contravariant derivative, Lie algebroid, Poisson algebra, Poisson cohomology, Poisson module, Poisson submanifold, Trivial extension algebra",

author = "D. Garc{\'i}a-Beltr{\'a}n and Ru{\'i}z-Pantale{\'o}n, {J. C.} and Yu Vorobiev",

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AU - García-Beltrán, D.

AU - Ruíz-Pantaleón, J. C.

AU - Vorobiev, Yu

PY - 2023/12

Y1 - 2023/12

N2 - 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.

AB - 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.

KW - Contravariant derivative

KW - Lie algebroid

KW - Poisson algebra

KW - Poisson cohomology

KW - Poisson module

KW - Poisson submanifold

KW - Trivial extension algebra

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VL - 54

JO - Bulletin of the Brazilian Mathematical Society

JF - Bulletin of the Brazilian Mathematical Society

IS - 4

M1 - 54

ER -

Poisson Structures on Trivial Extension Algebras

Abstract

Bibliographical note

Keywords

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