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A counterexample to the existence of a Poisson structure on a twisted group algebra

Eliana Zoque
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Abstract

Crawley-Boevey introduced the definition of a noncommutative Poisson structure on an associative algebra A that extends the notion of the usual Poisson bracket. Let V be a symplectic manifold and G be a finite group of symplectimorphisms of V. 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 on C[V]#G that extends the Poisson bracket on C[V]^G.

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Eliana Zoque. 2006-08-03. A counterexample to the existence of a Poisson structure on a twisted group algebra. https://arxiv.org/abs/math/0608099

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