REPRESENTATION THEORY AND RELATED TOPICS SEMINAR

Eliana Zoque

ABSTRACT:  Crawley-Boevey gave a definition of a noncommutative Poisson structure on an associative algebra that extends the usual definition for a commutative algebra. Let V be a symplectic manifold, endowed with the usual Poisson bracket on the commutative algebra of polynomials C[V]. Let G be a finite group of symplectimorphisms of V and consider the twisted group algebra A=C[V]#G. We produce a counterexample to prove that it is not always possible to define a noncommutative poisson structure in the sense of Crawley-Boevey on C[V]#G that extends the Poisson bracket on the algebra of invariant polynomials C[V]^G.