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

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

2006-03-23

arxiv.org/abs/math-ph/0603057v1

Physics

Mathematical Physics

Accepted for publication at the Journal of Nonlinear Mathematical Physics

Scientific paper

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 $\cS\Psi \cD \cO(S^{1\mid 2})$ 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.

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