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


SIGMA 8 (2012), 006, 14 pages      arXiv:1106.1512      http://dx.doi.org/10.3842/SIGMA.2012.006

On Lie Algebroids and Poisson Algebras

Dennise García-Beltrán a, José A. Vallejo a and Yuriĭ Vorobjev b
a) Facultad de Ciencias, Universidad Autónoma de San Luis Potosí, México
b) Departamento de Matemáticas, Universidad de Sonora, México

Received June 08, 2011, in final form February 01, 2012; Published online February 10, 2012

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.

Key words: transitive Lie algebroids; Lie-Rinehart algebras; Poisson brackets; algebraic connections.

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