The Canonical Differential Complex of Poisson Manifold and Distributions

TL;DR

This paper explores the homological structures of Poisson algebras, focusing on the canonical differential complex for singular Poisson structures, and introduces new interpretations and descriptions of invariant distributions.

Contribution

It introduces a novel interpretation of the Koszul differential as a supercommutator and describes the space of invariant distributions on singular Poisson manifolds.

Findings

Interpretation of Koszul differential as supercommutator

Description of invariant distributions on singular Poisson manifolds

Analysis of homological structures in Poisson algebra

Abstract

We study variuos homological structures associated with Poisson algebra, the canonical differential complex for singular Poisson structure and the analogue of the star operator for such manifolds. Give the interpretation of the classical Koszul differential of exterior forms, as the supercommutator with some second order element. Describe the space of invariant distributions on manifold with singular Poisson structure.