Deformation of sl(2) and osp(1|2)-Modules of Symbols

Abstract

We consider the sl(2)-module structure on the spaces of symbols of differential opera- tors acting on the spaces of weighted densities. We compute the necessary and sufficient integrability conditions of a given infinitesimal deformation of this structure and we prove that any formal deformation is equivalent to its infinitesimal part. We study also the super analogue of this problem getting the same results.

References in corpus (4)

• Differential operators on supercircle: conformally equivariant quantization and symbol calculus
• Cohomology of the Lie Superalgebra of Contact Vector Fields on ${\mathbb{R}}^{1|1}$ and Deformations of the Superspace of Symbols
• Cohomology of $\mathfrak{osp}(1|2)$ acting on linear differential operators on the supercircle $S^{1|1}
• Deformation of Vect($\mathbb{R})$-Modules of Symbols

Cited by in corpus (1)

• Deformation of $\mathfrak{osp}(2|2)$-Modules of Symbols