On matrix realizations of the contact superconformal algebra K'(4) and the exceptional N = 6 superconformal algebra

2007/07/20 by Elena Poletaeva, Poletaeva, Elena
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Nonlinear Waves and Solitons #hep-th

paper · pdf · doi:10.48550/arxiv.0707.3097

5 pages, LaTex, to be published in Dynamics of Continuous, Discrete and Impulsive Systems-Series A (Special Issue) in 2007

arxiv created 2007/07/20 · openalex publication_date 2007/07/20 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The superalgebra K'(4) and the exceptional N = 6 superconformal algebra have ``small'' irreducible representations in the superspaces V^μ = t^μ\C[t, t^-1]⊗Λ(N), where N = 2 and 3, respectively. For μ∈ \C\backslash \Z they are associated to the embeddings of these superalgebras into the Lie superalgebras of pseudodifferential symbols on the supercircle S^1|N. In this work we describe K'(4) and the exceptional N = 6 superconformal algebra in terms of matrices over a Weyl algebra. Correspondingly, we obtain realizations of their representations in V^μ for μ= 0.

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