Hochschild Cohomology and Deformations of Clifford-Weyl Algebras

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