Matrix realizations of exceptional superconformal algebras

Abstract

We give a general construction of realizations of the contact superconformal algebras $K(2)$ and ${\hat{K}}^{\prime }(4)$, and the exceptional superconformal algebra $C{K}_6$ as subsuperalgebras of matrices over a Weyl algebra of size $2^N\times 2^N$, where $N=1,2$ and $3$. We show that there is no such a realization for $K(2N)$, if $N\ge 4$.

arXiv comment17 pages, LaTeX, to be published in the Journal of Geometry and Physics

References in corpus (6)

• Lie superalgebras of string theories
• Classification of supersymmetries
• A spinor-like representation of the contact superconformal algebra K'(4)
• Embedding of the Lie superalgebra $D(2,1;\alpha )$ into the Lie superalgebra of pseudodifferential symbols on $S^{1|2}$
• On matrix realizations of the contact superconformal algebra ${\hat{K}}^{\prime }(4)$ and the exceptional N = 6 superconformal algebra
• On representations of the exceptional superconformal algebra $C{K}_6$

Cited by in corpus (1)

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