Quantum Lichnerowicz - Poisson complex

TL;DR

This paper introduces a quantum version of the Lichnerowicz differential using vertex algebra techniques, providing a new method to compute Poisson cohomology and invariants for Poisson manifolds.

Contribution

It develops a quantum analogue of the Lichnerowicz differential via the bc-beta-gamma system, enabling new approaches to Poisson cohomology and invariants.

Findings

Defines a quantum Lichnerowicz differential using vertex algebras.

Provides a new method for computing Lichnerowicz-Poisson cohomology groups.

Introduces a novel invariant for Poisson manifolds.

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.