Hochschild Cohomology and Deformations of Clifford-Weyl Algebras

Abstract

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 $k\ne 1$. We find all non-trivial deformations of $\mathcal{C}(2n+1,2)$ and study their representations.

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• Singular quadratic Lie superalgebras