A spinor-like representation of the contact superconformal algebra K'(4)

Abstract

In this work we construct an embedding of a nontrivial central extension of the contact superconformal algebra K'(4) into the Lie superalgebra of pseudodifferential symbols on the supercircle S^{1|2}. Associated with this embedding is a one-parameter family of spinor-like tiny irreducible representations of K'(4) realized just on 4 fields instead of the usual 16.

19 pages, TeX. Corrections to the references in the paper to be published in J. Math. Phys. v 42, no 1, 2001

References in corpus (3)

• Equivalence between Chain Categories of Representations of Affine sl(2) and N=2 Superconformal Algebras
• Deforming the Lie algebra of vector fields on $S^1$ inside the Poisson algebra on ${\dot{T}}^{\ast }{S}^1$
• Deforming the Lie algebra of vector fields on $S^1$ inside the Lie algebra of pseudodifferential symbols on $S^1$

Cited by in corpus (4)

• Non-degenerate invariant (super)symmetric bilinear forms on simple Lie (super)algebras
• Embedding of the Lie superalgebra $D(2,1;\alpha )$ into the Lie superalgebra of pseudodifferential symbols on $S^{1|2}$
• Matrix realizations of exceptional superconformal algebras
• On cohomology of the Lie superalgebra D(2, 1 ; α)