The relative cohomology of the Lie superalgebra of contact vector fields on S1|2

Abstract

Over the [Formula: see text]-dimensional supercircle [Formula: see text], we investigate the first [Formula: see text]-relative cohomology space associated with the embedding of the Lie superalgebra [Formula: see text] of contact vector fields in the Lie superalgebra [Formula: see text] of superpseudodifferential operators with smooth coefficients, where [Formula: see text] is the orthosymplectic Lie superalgebra. Likewise, we study the same problem for the affine Lie superalgebra [Formula: see text] instead of [Formula: see text]. We classify generic formal [Formula: see text]-trivial deformations of the [Formula: see text]-module structure on the superspace of the supercommutative algebra [Formula: see text] of pseudodifferential symbols on [Formula: see text].

osp(1|2)-trivial deformation of osp(2Almoneef, Abdaoui, Ghallabi 2024Heliyon0000View full textAdd to dashboardCite

“…Lie algebra homomorphism deformation theory was initially thought of using just one deformation parameter [18] , [20] . Recently, there has been a lot of research done on Lie (super)algebra deformations with several parameters (see, e.g., [1] , [2] , [4] , [7] , [10] , [11] , [14] , [19] ). This section provides a summary of this theory.…”

“…In 2012, Basdouri and Ben Ammar [5] classified the deformation of -modules and -modules of symbols. In 2018, Ben Fraj, Abdaoui and Raouafi [11] classified the deformations of -modules of symbols trivial on . They are proved that the conditions of integrability of the infinitesimal deformation of the second order are necessary and sufficient.…”