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

Abstract

We investigate the first cohomology space associated with the embedding of the Lie superalgebra $\cK(2)$ of contact vector fields on the (1,2)-dimensional supercircle $S^{1\mid 2}$ in the Lie superalgebra $\cSΨ\cD \cO(S^{1\mid 2})$ of superpseudodifferential operators with smooth coefficients. Following Ovsienko and Roger, we show that this space is ten-dimensional with only even cocycles and we give explicit expressions of the basis cocycles.

Accepted for publication at the Journal of Nonlinear Mathematical Physics

References in corpus (1)

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

Cited by in corpus (5)

• Cohomology of the Lie Superalgebra of Contact Vector Fields on ${\mathbb{R}}^{1|1}$ and Deformations of the Superspace of Symbols
• On the Cohomology of the Lie Superalgebra of Contact Vector Fields on $S^{1|2}$
• Conformal symbols and the action of contact vector fields over the superline
• Differential Operators on the Weighted Densities on the Supercircle $S^{1|n}$
• On cohomology of the Lie superalgebra D(2, 1 ; α)