This article is cited in 3 papers

On Lie algebroids and Poisson algebras

Dennise García-Beltrán^a, José A. Vallejo^a, Yuriĭ Vorobjev<sup>b

a</sup> Facultad de Ciencias, Universidad Autónoma de San Luis Potosí
^b Departamento de Matemáticas, Universidad de Sonora, México

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: transitive Lie algebroids, Lie–Rinehart algebras, Poisson brackets, algebraic connections.

MSC: 53D17, 17B63

Received: June 8, 2011; in final form February 1, 2012; Published online February 10, 2012

Language: English

DOI: 10.3842/SIGMA.2012.006

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ArXiv: 1106.1512