Homology, Homotopy and Applications
Volume 24 (2022)
Symmetric Hochschild cohomology of twisted group algebras
Pages: 93 – 115
We show that there is an action of the symmetric group on the Hochschild cochain complex of a twisted group algebra with coefficients in a bimodule. This allows us to define the symmetric Hochschild cohomology of twisted group algebras, similarly to Staic’s construction of symmetric group cohomology.We give explicit embeddings and connecting homomorphisms between the symmetric cohomology spaces and symmetric Hochschild cohomology of twisted group algebras.
Hochschild cohomology, symmetric group, group cohomology, connecting homomorphism, twisted group algebra
2010 Mathematics Subject Classification
This work was supported by a grant of the Ministry of Research, Innovation and Digitization, CNCS/CCCDI-UEFISCDI, project number PN-III-P1-1.1-TE-2019-0136, within PNCDI III.
Received 12 August 2020
Received revised 30 November 2020
Accepted 25 February 2021
Published 30 March 2022