Deforming the Lie Superalgebra $\mathcal{K}(1)$-Modules Of Symbols

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dc.creatorFaouzi, Ammar
dc.creatorKaouthar, Kamoun
dc.date2008-07-30
dc.date.accessioned2026-07-07T09:53:42Z
dc.date.available2026-07-07T09:53:42Z
dc.descriptionWe study non-trivial deformations of the natural action of the Lie superalgebra $mathcalK(1)$ of contact vector fields on the (1,1)-dimensional superspace $mathbbR^{1|1}$ of th espace of symbols. We calculate obstructions for integrability of infinitesimal multi-parameter deformation and determine the complete commutative algebra corresponding to the miniversal deformation in the sense of A. Fialowski. Besides, we compute the first even differential cohomology space $mathrmH^1_{mathrm{diff}}(cK(1);widetilde{cD}_{lambda,mu})$ of the Lie superalgebra $mathcalK(1)$ of contact vector fields on the (1,1)-dimensional superspace $mathbbR^{1|1}$ with coefficients in the superspace $widetilde{mathcalD}_{lambda,mu}$ of linear differential operators from the superspace of weighted densities $\fF_{\lamda}$ to $\fF_μ$. (To appear in Journal of Generalized Lie Theory and Applications)
dc.identifierhttps://arxiv.org/abs/0807.4811
dc.identifierhttp://arxiv.org/abs/0807.4811
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/166049
dc.subjectMathematical Physics
dc.titleDeforming the Lie Superalgebra $\mathcal{K}(1)$-Modules Of Symbols
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