Hochschild Cohomology and Deformations of Clifford-Weyl Algebras

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2009
• Main Authors: Musson, I.M., Pinczon, G., Ushirobira, R.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2009
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/149177
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Hochschild Cohomology and Deformations of Clifford-Weyl Algebras / I.M. Musson, G. Pinczon, R. Ushirobira // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 28 назв. — англ.

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.