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SIGMA, 2012, Volume 8, 006, 14 pages (Mi sigma683)  

On Lie algebroids and Poisson algebras

Dennise García-Beltrána, José A. Vallejoa, Yuriĭ Vorobjevb

a 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.

DOI: https://doi.org/10.3842/SIGMA.2012.006

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Full text: http://emis.mi.ras.ru/.../006
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Bibliographic databases:

ArXiv: 1106.1512
MSC: 53D17, 17B63
Received: June 8, 2011; in final form February 1, 2012; Published online February 10, 2012
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Citation: Dennise García-Beltrán, José A. Vallejo, Yuriǐ Vorobjev, “On Lie algebroids and Poisson algebras”, SIGMA, 8 (2012), 006, 14 pp.

Citation in format AMSBIB
\Bibitem{GarValVor12}
\by Dennise Garc{\'\i}a-Beltr\'an, Jos\'e A. Vallejo, Yuri{\v\i} Vorobjev
\paper On Lie algebroids and Poisson algebras
\jour SIGMA
\yr 2012
\vol 8
\papernumber 006
\totalpages 14
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\crossref{https://doi.org/10.3842/SIGMA.2012.006}
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