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

Over the (1 , 2) -dimensional supercircle S 1 | 2 , we investigate the first 𝔬 𝔰 𝔭 (2 | 2) -relative cohomology space associated with the embedding of the Lie superalgebra 𝒦 (2) of contact vector fields in the Lie superalgebra 𝒮 Ψ 𝒟 𝒪 (S 1 | 2) of superpseudodifferential operators with smooth coefficients, where 𝔬 𝔰 𝔭 (2 | 2) is the orthosymplectic Lie superalgebra. Likewise, we study the same problem for the affine Lie superalgebra 𝔞 𝔣 𝔣 (2 | 1) instead of 𝔬 𝔰 𝔭 (2 | 2). We classify generic formal 𝔬 𝔰 𝔭 (2 | 2) -trivial deformations of the 𝒦 (2) -module structure on the superspace of the supercommutative algebra 𝒮 𝒫 (2) of pseudodifferential symbols on S 1 | 2 . [ABSTRACT FROM AUTHOR]