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