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Lichnerowicz-Jacobi cohomology

AuthorsLeón, Manuel de; Marrero, Juan Carlos; Padrón, Edith
Issue Date1997
PublisherInstitute of Physics Publishing
CitationJournal of Physics A: Mathematical and General 30: 6029- 6055 (1997)
AbstractIn this paper we extend the notion of Lichnerowicz-Poisson cohomology to Jacobi manifolds. We study the relation of the so-called Lichnerowicz-Jacobi cohomology with the basic de Rham cohomology and the cohomology of the Lie algebra of functions relative to the representation defined by the Hamiltonian vector fields. A natural pairing with the canonical homology is constructed. The relation between the Lichnerowicz-Poisson cohomology of a quantizable Poisson manifold and the Lichnerowicz-Jacobi cohomology of the total space of a prequantization bundle is obtained. Particular cases of cosymplectic, contact and locally conformal symplectic manifolds are discussed. Finally, the Lichnerowicz-Jacobi cohomology of a non-transitive example is studied. c 1997 IOP Publishing Ltd
Identifiersdoi: 10.1088/0305-4470/30/17/014
issn: 0305-4470
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