Embedding of the Lie superalgebra $D(2,1;\alpha )$ into the Lie superalgebra of pseudodifferential symbols on $S^{1|2}$

Abstract

We obtain an embedding of a one-parameter family of exceptional simple Lie superalgebras $D(2,1;\alpha )$ into the Lie superalgebra of pseudodifferential symbols on the supercircle $S^{1|2}$. Correspondingly, there is an embedding of $D(2,1;\alpha )$ into a nontrivial central extension of the derived contact superconformal algebra $K^{\prime }(4)$ realized in terms of $4\times 4$ matrices over a Weyl algebra.

19 pages, LaTex, to be published in J.Math. Phys

Cited by in corpus (2)

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