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arXiv · 0709.0083

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

Elena Poletaeva
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Abstract

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

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Elena Poletaeva. 2007-09-01. Embedding of the Lie superalgebra $D(2, 1 ; α)$ into the Lie superalgebra of pseudodifferential symbols on $S^{1|2}$. https://doi.org/10.1063/1.2793570

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