Homology, Homotopy and Applications

Volume 24 (2022)

Number 1

Symmetric Hochschild cohomology of twisted group algebras

Pages: 93 – 115

DOI: https://dx.doi.org/10.4310/HHA.2022.v24.n1.a5

Authors

Tiberiu Coconeţ (Faculty of Economics and Business Administration, Babeş-Bolyai University, Cluj-Napoca, Romania; and Department of Mathematics, Technical University of Cluj-Napoca, Romania)

Constantin-Cosmin Todea (Department of Mathematics, Technical University of Cluj-Napoca, Romania)

Abstract

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.

Keywords

Hochschild cohomology, symmetric group, group cohomology, connecting homomorphism, twisted group algebra

2010 Mathematics Subject Classification

16E40, 20J06

Full Text (PDF format)

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