Cohomology of Lie superalgebras slm|n and osp2|2n

Proceedings of the London Mathematical Society (Impact Factor: 1.12). 11/2006; DOI: 10.1112/plms/pdl005
Source: OAI

ABSTRACT We explicitly compute the first and second cohomology groups of the classical Lie superalgebras 𝔰𝔩 m | n and 𝔬𝔰𝔬 2|2 n with coefficients in the finite-dimensional irreducible modules and the Kac modules. We also show that the second cohomology groups of these Lie superalgebras with coefficients in the respective universal enveloping algebras (under the adjoint action) vanish. The latter result, in particular, implies that the universal enveloping algebras U(𝔰𝔩 m | n ) and U(𝔬𝔰𝔭 2|2 n ) do not admit any non-trivial formal deformations of Gerstenhaber type.