Hochschild Cohomology and Deformations of Clifford-Weyl Algebras

2008/10/31 by Ian M. Musson, Georges Pinczon, Rosane Ushirobira · 1 citation
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #math-ph #math.MP #math.RA #math.RT #msc:17B10 #msc:17B56

paper · pdf · doi:10.3842/sigma.2009.028

published as SIGMA 5 (2009), 028, 27 pages

openalex publication_date 2009/03/07 · arxiv created 2009/03/18 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Symplectic reflection algebras, Calogero-Moser space, and deformed Harish-Chandra homomorphism

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