Symmetric Hochschild cohomology of twisted group algebras (Q2670953)

In this paper, the authors prove that there is an action of the symmetric group on the Hochschild cochain complex of a twisted group algebra with coefficients in a bimodule. First, the authors review basic facts about Hochschild cohomology and group cohomology. Then they show that there is a well-defined action of the symmetric group on the Hochschild cochain complex. This allows the authors to define the symmetric Hochschild cohomology for twisted group algebra. Applications of this approach are also discussed.