On Lie algebroids and Poisson algebras

Dennise García-Beltrán; José A. Vallejo; Yuriǐ Vorobjev

doi:10.3842/SIGMA.2012.006

On Lie algebroids and Poisson algebras

Dennise García-Beltrán^*, José A. Vallejo, Yuriǐ Vorobjev

^*Corresponding author for this work

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

3 Scopus citations

Abstract

We introduce and study a class of Lie algebroids associated to faithful modules which is motivated by the notion of cotangent Lie algebroids of Poisson manifolds. We also give a classification of transitive Lie algebroids and describe Poisson algebras by using the notions of algebroid and Lie connections.

Original language	English
Article number	006
Journal	Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
Volume	8
DOIs	https://doi.org/10.3842/SIGMA.2012.006
State	Published - 10 Feb 2012

Keywords

Algebraic connections
Lie-Rinehart algebras
Poisson brackets
Transitive Lie algebroids

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10.3842/SIGMA.2012.006

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title = "On Lie algebroids and Poisson algebras",

abstract = "We introduce and study a class of Lie algebroids associated to faithful modules which is motivated by the notion of cotangent Lie algebroids of Poisson manifolds. We also give a classification of transitive Lie algebroids and describe Poisson algebras by using the notions of algebroid and Lie connections.",

keywords = "Algebraic connections, Lie-Rinehart algebras, Poisson brackets, Transitive Lie algebroids",

author = "Dennise Garc{\'i}a-Beltr{\'a}n and Vallejo, {Jos{\'e} A.} and Yuriǐ Vorobjev",

year = "2012",

month = feb,

day = "10",

doi = "10.3842/SIGMA.2012.006",

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AU - García-Beltrán, Dennise

AU - Vallejo, José A.

AU - Vorobjev, Yuriǐ

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Y1 - 2012/2/10

N2 - We introduce and study a class of Lie algebroids associated to faithful modules which is motivated by the notion of cotangent Lie algebroids of Poisson manifolds. We also give a classification of transitive Lie algebroids and describe Poisson algebras by using the notions of algebroid and Lie connections.

AB - We introduce and study a class of Lie algebroids associated to faithful modules which is motivated by the notion of cotangent Lie algebroids of Poisson manifolds. We also give a classification of transitive Lie algebroids and describe Poisson algebras by using the notions of algebroid and Lie connections.

KW - Algebraic connections

KW - Lie-Rinehart algebras

KW - Poisson brackets

KW - Transitive Lie algebroids

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U2 - 10.3842/SIGMA.2012.006

DO - 10.3842/SIGMA.2012.006

M3 - Artículo

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JO - Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

JF - Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

M1 - 006

ER -

On Lie algebroids and Poisson algebras

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Keywords

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