On matrix realizations of the contact superconformal algebra ${\hat{K}}^{\prime }(4)$ and the exceptional N = 6 superconformal algebra

Abstract

The superalgebra ${\hat{K}}^{\prime }(4)$ and the exceptional N = 6 superconformal algebra have ``small'' irreducible representations in the superspaces $V^μ = t^μ\C[t, t^{-1}]\otimesΛ(N)$, where N = 2 and 3, respectively. For ${μ\in \C\backslash \Z}$ 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 ${\hat{K}}^{\prime }(4)$ and the exceptional N = 6 superconformal algebra in terms of matrices over a Weyl algebra. Correspondingly, we obtain realizations of their representations in $V^{\mu }$ for $\mu =0$.

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

References in corpus (1)

• Classification of supersymmetries

Cited by in corpus (2)

• Matrix realizations of exceptional superconformal algebras
• On matrix realizations of the Lie superalgebra D(2, 1 ; α)