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

Abstract

We study non-trivial deformations of the natural action of the Lie superalgebra $mathcalK(1)$ of contact vector fields on the (1,1)-dimensional superspace $mathbb{R}^{1|1}$ 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 $mathrm{H}_{mathrmdiff}^1(cK(1);widetilde{cD}_{lambda,mu})$ of the Lie superalgebra $mathcalK(1)$ of contact vector fields on the (1,1)-dimensional superspace $mathbb{R}^{1|1}$ 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)

References in corpus (1)

• Deforming the Lie algebra of vector fields on $S^1$ inside the Poisson algebra on ${\dot{T}}^{\ast }{S}^1$