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].