Journal of Generalized Lie Theory and Applications

Deforming $\mathcal{K}(1) $ superalgebra modules of symbols

Faouzi AMMAR and Kaouthar KAMOUN

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Abstract

We study nontrivial deformations of the natural action of the Lie superalgebra $\mathcal{K}(1)$ of contact vector fields on the $(1,1)$-dimensional superspace $\mathbb{R}^{1|1}$ on the space of symbols $\widetilde{{\mathcal{S}}}_\delta^n=\bigoplus_{k=0}^n{\mathfrak{F}}_{\delta-\frac{k}{2}}$. We calculate obstructions for integrability of infinitesimal multiparameter deformations and determine the complete local commutative algebra corresponding to the miniversal deformation.

Article information

Source
J. Gen. Lie Theory Appl., Volume 3, Number 2 (2009), Article ID S090202, 95-111.

Dates
First available in Project Euclid: 7 October 2011

Permanent link to this document
https://projecteuclid.org/euclid.jglta/1318008547

Digital Object Identifier
doi:10.4303/jglta/S090202

Mathematical Reviews number (MathSciNet)
MR2504872

Zentralblatt MATH identifier
1230.17016

Citation

AMMAR, Faouzi; KAMOUN, Kaouthar. Deforming $\mathcal{K}(1) $ superalgebra modules of symbols. J. Gen. Lie Theory Appl. 3 (2009), no. 2, Article ID S090202, 95--111. doi:10.4303/jglta/S090202. https://projecteuclid.org/euclid.jglta/1318008547


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