hal-00021590, version 1
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 $\cS\Psi \cD \cO(S^{1\mid 2})$ 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.
- 1:
- Faculté des sciences de Sfax
- Domain : Mathematics/Mathematical Physics
- Comment : Accepted for publication at the Journal of Nonlinear Mathematical Physics
- hal-00021590, version 1
- http://hal.archives-ouvertes.fr/hal-00021590
- oai:hal.archives-ouvertes.fr:hal-00021590
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- Submitted on: Wednesday, 22 March 2006 18:23:51
- Updated on: Thursday, 23 March 2006 09:00:20
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