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

^*Autor correspondiente de este trabajo

Producción científica: Contribución a una revista › Artículo › revisión exhaustiva

Resumen

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.

Idioma original	Inglés
Número de artículo	54
Publicación	Bulletin of the Brazilian Mathematical Society
Volumen	54
N.º	4
DOI	https://doi.org/10.1007/s00574-023-00366-4
Estado	Publicada - dic. 2023

Nota bibliográfica

Publisher Copyright:
© 2023, The Author(s), under exclusive licence to Brazilian Mathematical Society.

Acceder al documento

10.1007/s00574-023-00366-4

Otros archivos y enlaces

Enlace a la publicación en Scopus

Citar esto

@article{cd275027048a4369aa67a6e073c562cc,

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",

note = "Publisher Copyright: {\textcopyright} 2023, The Author(s), under exclusive licence to Brazilian Mathematical Society.",

year = "2023",

month = dec,

doi = "10.1007/s00574-023-00366-4",

language = "Ingl{\'e}s",

volume = "54",

journal = "Bulletin of the Brazilian Mathematical Society",

issn = "1678-7544",

publisher = "Springer New York",

number = "4",

}

TY - JOUR

T1 - Poisson Structures on Trivial Extension Algebras

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

UR - http://www.scopus.com/inward/record.url?scp=85173649923&partnerID=8YFLogxK

U2 - 10.1007/s00574-023-00366-4

DO - 10.1007/s00574-023-00366-4

M3 - Artículo

AN - SCOPUS:85173649923

SN - 1678-7544

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

Resumen

Nota bibliográfica

Acceder al documento

Otros archivos y enlaces

Huella

Citar esto