This article is based on the author’s talk at international conference dedicated to memory of Professor B. Yu. Sternin (Moscow, November 6–9, 2018). The Hochschild homology and cohomology a group algebra can be described via classifying space adjoint action groupoid under suitable assumption finiteness supports groups. difference between leads correction results in D. J. Benson’s book Represent...

We consider a finite group acting on a vector space and the corresponding skew group algebra generated by the group and the symmetric algebra of the space. This skew group algebra illuminates the resulting orbifold and serves as a replacement for the ring of invariant polynomials, especially in the eyes of cohomology. One analyzes the Hochschild cohomology of the skew group algebra using isomor...

We show that there is an action of the symmetric group on Hochschild cochain complex a twisted algebra with coefficients in bimodule. This allows us to define cohomology algebras, similarly th construction due Staic. give explicit embeddings and connecting homomorphisms between spaces algebras.