Let be the orthosymplectic Lie superalgebra and a Lie subalgebra of . In our paper, we describe the cup-product , where is the first differential -relative cohomology of with coefficients in and is the space of linear differential operators acting on weighted densities. This result allows us to classify the -trivial deformations of the -module structure on the spaces of symbols . More precisely, we compute the necessary and sufficient integrability conditions of a given infinitesimal deformation of this action. Furthermore, we prove that any formal -trivial deformations of -modules of symbols is equivalent to its infinitisemal part. This work is the simplest generalization of a result by Laraiedh [17].
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| http://www.ncbi.nlm.nih.gov/pmc/articles/PMC11154194 | PMC |
| http://dx.doi.org/10.1016/j.heliyon.2024.e31660 | DOI Listing |
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