Algebra Seminar: Wu -- BV-algebra structure over Poisson cohomology

Quanshui Wu (Fudan University) 

Friday 10 February, 12-1pm, Place: Carslaw 375 

BV-algebra structure over Poisson cohomology.  

Similar to the modular vector fields in Poisson geometry, modular derivations can be
defined for smooth Poisson algebras with trivial canonical bundle.  By twisting Poisson
modules with the modular derivation, the Poisson cochain complex with values in any
Poisson module is isomorphic to the Poisson chain complex with values in the
corresponding twisted Poisson module.  Then a version of twisted Poincare duality is
deduced between Poisson homologies and Poisson cohomologies.  If the Poisson structure
is unimodular, then its Poisson cohomology as Gerstenhaber algebra is exact, that is, it
has a Batalin-Vilkovisky algebra structure by using the isomorphism between the Poisson
cochain complex and chain complex.