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Register a new userComputations of the Hochschild Cohomology of Group Algebras
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Authors
Adam A. Allan
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The Hochschild cohomology ring of a group algebra is an object that has received recent attention, but is difficult to compute, in even the simplest of cases. In this paper, we use the product formula due to Witherspoon and Siegel to extend some of their computations. In particular, we compute the Hochschild cohomology algebra of group algebras kG where |G| is less than 16, and we provide an alternative computation of the ring $HH^*(k(E ltimes P))$ considered by Kessar and Linckelmann.
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We give a complete study of the Clifford-Weyl algebra ${mathcal C}(n,2k)$ from Bose-Fermi statistics, including Hochschild cohomology (with coefficients in itself). We show that ${mathcal C}(n,2k)$ is rigid when $n$ is even or when $k eq 1$. We find all non-trivial deformations of ${mathcal C}(2n+1,2)$ and study their representations.
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