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 $k\neq1$. We find all non-trivial deformations of $\mathcal C(2n+1,2)$ and study their representations.