Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 5 (2009), 028, 27 pages      arXiv:0810.0184      https://doi.org/10.3842/SIGMA.2009.028
Contribution to the Special Issue on Deformation Quantization

Hochschild Cohomology and Deformations of Clifford-Weyl Algebras

Ian M. Musson a, Georges Pinczon b and Rosane Ushirobira b
a) Department of Mathematical Sciences, University of Wisconsin-Milwaukee, Milwaukee, WI 53201-0413, USA
b) Institut de Mathématiques de Bourgogne, Université de Bourgogne, B.P. 47870, F-21078 Dijon Cedex, France

Received October 01, 2008, in final form February 25, 2009; Published online March 07, 2009

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.

Key words: Hochschild cohomology; deformation theory; Clifford algebras; Weyl algebras; Clifford-Weyl algebras; parastatistics.

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