2013/07/19 by N. Aizawa, Zhanna Kuznetsova, Z. Kuznetsova +2 · 2 citations
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #hep-th #math-ph #math.MP
paper · pdf · doi:10.1063/1.4820481
published as J. Math. Phys. 54 (2013) 093506 · 14 pages
arxiv created 2013/07/19 · openalex publication_date 2013/09/01 · arxiv updated 2013/09/23 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
Inequivalent \documentclass[12pt]minimal\begindocument\cal N=2\enddocumentN=2 supersymmetrizations of the ℓ-conformal Galilei algebra in d-spatial dimensions are constructed from the chiral (2, 2) and the real (1, 2, 1) basic supermultiplets of the \documentclass[12pt]minimal\begindocument\cal N=2\enddocumentN=2 supersymmetry. For non-negative integer and half-integer ℓ, both superalgebras admit a consistent truncation with a (different) finite number of generators. The real \documentclass[12pt]minimal\begindocument\cal N=2\enddocumentN=2 case coincides with the superalgebra introduced by Masterov, while the chiral \documentclass[12pt]minimal\begindocument\cal N=2\enddocumentN=2 case is a new superalgebra. We present D-module representations of both superalgebras. Then we investigate the new superalgebra derived from the chiral supermultiplet. It is shown that it admits two types of central extensions, one is found for any d and half-integer ℓ, and the other only for d = 2 and integer ℓ. For each central extension, the centrally extended ℓ-superconformal Galilei algebra is realized in terms of its super-Heisenberg subalgebra generators.