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

Abstract

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 $K^{\prime }(4)$, the infinitesimal deformations are formal deformations.

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

References in corpus (2)

• On the Cohomology of the Lie Superalgebra of Contact Vector Fields on $S^{1|2}$
• Classification of supersymmetries