On the geometric prequantization of brackets

In this paper we consider a general setting for geometric prequantization of a manifold endowed with a non-necessarily Jacobi bracket. The existence of a generalized foliation permits to define a notion of prequantization bundle. A second approach is given assuming the existence of a Lie algebroid o...

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Detalles Bibliográficos
Autores: León, Manuel de, Marrero, Juan Carlos, Padrón, Edith
Tipo de recurso: artículo
Fecha de publicación:2001
País:España
Institución:Consejo Superior de Investigaciones Científicas (CSIC)
Repositorio:DIGITAL.CSIC. Repositorio Institucional del CSIC
OAI Identifier:oai:digital.csic.es:10261/2229
Acceso en línea:http://hdl.handle.net/10261/2229
Access Level:acceso abierto
Palabra clave:Jacobi manifolds
Poisson manifolds
Lie algebroids
H-Chevalley-Eilenberg cohomology
Lichnerowicz-Jacobi cohomology
Lichnerowicz-Poisson cohomology
Foliated cohomology
Foliated covariant derivatives
Geometric prequantization
Descripción
Sumario:In this paper we consider a general setting for geometric prequantization of a manifold endowed with a non-necessarily Jacobi bracket. The existence of a generalized foliation permits to define a notion of prequantization bundle. A second approach is given assuming the existence of a Lie algebroid on the manifold. Both approaches are related, and the results for Poisson and Jacobi manifolds are recovered.