Twisted Poincare duality between Poisson homology and Poisson cohomology

摘要

A version of the twisted Poincare duality is proved between the Poisson homology and cohomology of a polynomial Poisson algebra with values in an arbitrary Poisson module. The duality is achieved by twisting the Poisson module structure in a canonical way, which is constructed from the modular derivation. In the case that the Poisson structure is unimodular, the twisted Poincare duality reduces to the Poincare duality in usual sense. The main result generalizes the work of Launois and Richard [8] for the quadratic Poisson structures and Zhu [25] for the linear Poisson structures. (C) 2014 Elsevier Inc. All rights reserved.