Quantum Lichnerowicz - Poisson complex

Abstract

Using the curved bc-beta-gamma system (a tensor product of a Heisenberg and a Clifford vertex algebra) we introduce quantum analogy of Lichnerowicz differential. As follows we suggest new machinery for finding the Lichnerowicz-Poisson cohomology groups for any Poisson manifold. Moreover, the defined provides new invariant. Keywords: Poisson manifold, Lichnerowicz differential, Chiral de Rham complex, cohomologies, vertex algebras, deformation theory, Nambu-Poisson bracket, n-Lie algebras, Gromov-Witten theory.