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Symmetry, Integrability and Geometry: Methods and Applications, 2009, Volume 5, 028, 27 pp.
DOI: https://doi.org/10.3842/SIGMA.2009.028 (Mi sigma374) 		 
This article is cited in 5 scientific papers (total in 5 papers)

Hochschild Cohomology and Deformations of Clifford–Weyl Algebras

Ian M. Mussona, Georges Pinczonb, Rosane Ushirobirab

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
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DOI: https://doi.org/10.3842/SIGMA.2009.028
Abstract: 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.
Keywords: Hochschild cohomology; deformation theory; Clifford algebras; Weyl algebras; Clifford–Weyl algebras; parastatistics.
Received: October 1, 2008; in final form February 25, 2009; Published online March 7, 2009
Bibliographic databases:
Document Type: Article
MSC: 16E40; 16G99; 16S80; 17B56; 17B10; 53D55
Language: English
Citation: Ian M. Musson, Georges Pinczon, Rosane Ushirobira, “Hochschild Cohomology and Deformations of Clifford–Weyl Algebras”, SIGMA, 5 (2009), 028, 27 pp.
Citation in format AMSBIB
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\paper Hochschild Cohomology and Deformations of Clifford--Weyl Algebras
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