Hochschild Cohomology and Deformations of Clifford-Weyl Algebras

Abstract

We give a complete study of the Clifford-Weyl algebra C(n,2k) from Bose-Fermi statistics, including Hochschild cohomology (with coefficients in itself). We show that C(n,2k) is rigid when n is even or when k ≠ 1. We find all non-trivial deformations of C(2n+1,2) and study their representations.

Keywords

• Hochschild cohomology
• deformation theory
• Clifford algebras
• Weyl algebras
• Clifford-Weyl algebras
• parastatistics