Cohomology of 𝔞𝔣𝔣(1|1) acting on the space of n-ary linear differential operators on S1|1

Abstract

We consider the spaces F µ of polynomial µ-densities on the line as sl(2)-modules and then we compute the cohomological spaces H 1 diff (sl (2), Dλ ,µ ), where µ ∈ R,λ = (λ 1 , . . . , λ n ) ∈ R n and Dλ ,µ is the space of n-ary differential operators from F λ1 ⊗· · ·⊗F λn to F µ .Mathematics Subject Classification (2010). 17B56