Twisted Poincar\'{e} duality between Poisson homology and Poisson cohomology
- Resource Type
- Working Paper
- Authors
- Luo, J.; Wang, S. -Q.; Wu, Q. -S.
- Source
- Subject
- Mathematics - Rings and Algebras
17B63, 17B55, 13D04, 16E40
- Language
A version of the twisted Poincar\'{e} 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 Poincar\'{e} duality reduces to the Poincar\'{e} duality in the usual sense. The main result generalizes the work of Launois-Richard \cite{LR} for the quadratic Poisson structures and Zhu \cite{Zhu} for the linear Poisson structures.
Comment: 18 pages