Abstract
In 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.
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