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SIGMA, 2009, Volume 5, 028, 27 pages (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

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

DOI: https://doi.org/10.3842/SIGMA.2009.028

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Bibliographic databases:

ArXiv: 0810.0184
Document Type: Article
MSC: 16E40; 16G99; 16S80; 17B56; 17B10; 53D55
Received: October 1, 2008; in final form February 25, 2009; Published online March 7, 2009
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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\by Ian M.~Musson, Georges Pinczon, Rosane Ushirobira
\paper Hochschild Cohomology and Deformations of Clifford--Weyl Algebras
\jour SIGMA
\yr 2009
\vol 5
\papernumber 028
\totalpages 27
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\crossref{https://doi.org/10.3842/SIGMA.2009.028}
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    This publication is cited in the following articles:
    1. Bieliavsky P. de Goursac A. Tuynman G., “Deformation Quantization for Heisenberg Supergroup”, J. Funct. Anal., 263:3 (2012), 549–603  crossref  mathscinet  zmath  isi  scopus
    2. Michel J.-P., “Conformal Geometry of the Supercotangent and Spinor Bundles”, Commun. Math. Phys., 312:2 (2012), 303–336  crossref  mathscinet  zmath  adsnasa  isi  scopus
    3. Herscovich, E, “Representations of Super Yang–Mills Algebras”, Communications in Mathematical Physics, 320:3 (2013), 783–820  crossref  mathscinet  zmath  adsnasa  isi  scopus
    4. Minh Thanh Duong, Ushirobira R., “Singular Quadratic Lie Superalgebras”, J. Algebra, 407 (2014), 372–412  crossref  mathscinet  zmath  isi  scopus
    5. Pandzic P., Somberg P., “Dirac Operator and Its Cohomology For the Quantum Group U-Q(Sl(2))”, J. Math. Phys., 58:4 (2017), 041702  crossref  mathscinet  zmath  isi  scopus
  • Symmetry, Integrability and Geometry: Methods and Applications
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