Vol. 89, No. 1, 1980

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Sweedler’s two-cocycles and Hochschild cohomology

Dave Riffelmacher

Vol. 89 (1980), No. 1, 181–188

For any algebra C over a commutative ring k Sweedler defined a cohomology set which generalizes Amitsur’s second cohomology group H2(C∕k). Any Sweedler C-two-cocycle σ gives rise to a change of rings functor ( )σ from the category of C-bimodules to the category of Cσ-bimodules, where Cσ is the k-algebra with multiplication altered by σ, which in turn induces a map ϕn(σ,M) : Hn(C,M) Hn(Cσ,Mσ) on Hochschild cohomology for any C-bimodule M and any positive integer n. In this paper, several properties of ϕn(σ,M) are derived, including: If C is a finite dimensional algebra over a field k, ϕ1(σ,M) is an injection for all σ and M.

Mathematical Subject Classification
Primary: 16A62, 16A62
Secondary: 16A46
Received: 29 March 1979
Published: 1 July 1980
Dave Riffelmacher