On cohomology of the Lie superalgebra D(2, 1 ; α)

Details On cohomology of the Lie superalgebra D(2, 1 ; α) On cohomology of the Lie superalgebra D(2, 1 ; α)

2010-08-14

arxiv.org/abs/1008.2462v1

Mathematics

Representation Theory

17 pages, to be published in Journal of Geometry and Physics 60(2010), 1771-1780

Scientific paper

10.1016/j.geomphys.2010.06.015

We describe the infinitesimal deformations of the standard embedding of the Lie superalgebra $D(2, 1 ; \alpha)$ into the Poisson superalgebra of pseudodifferential symbols on $S^{1|2}$. We show that for the standard embedding of $D(2, 1 ; \alpha)$ into the Poisson superalgebra of differential operators on $S^{1|2}$, the infinitesimal deformations correspond to formal deformations. For the embedding of $D(2, 1 ; \alpha)$ into the derived contact superconformal algebra ${K}'(4)$, the infinitesimal deformations are formal deformations.

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