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

Boujemaa Agrebaoui·Nizar Ben Fraj·Salem Omri
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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 $\cS\Psi \cD \cO(S^{1\mid 2})$ 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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Boujemaa Agrebaoui, Nizar Ben Fraj, Salem Omri. 2006-03-23. On the Cohomology of the Lie Superalgebra of Contact Vector Fields on $S^{1|2}$. https://doi.org/10.2991/jnmp.2006.13.4.7

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