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

Authors

  • Eliana Zoque The University of Chicago Department of Mathematics

DOI:

https://doi.org/10.11606/issn.2316-9028.v3i1p109-113

Abstract

Crawley-Boevey [1] introduced the definition of a noncommutative Poisson structure on an associative algebra

A that extends the notion of the usual Poisson bracket. Let (V, w) be a symplectic mani-fold 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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Published

2009-06-30

Issue

Section

Articles

How to Cite

A counterexample to the existence of a Poisson structure on a twisted group algebra. (2009). The São Paulo Journal of Mathematical Sciences, 3(1), 109-113. https://doi.org/10.11606/issn.2316-9028.v3i1p109-113