Article

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

01/2006; DOI: 10.1112/plms/pdl005
Source: OAI

ABSTRACT We explicitly compute the first and second cohomology groups of the classical Lie superalgebras &sfr;&lfr; m | n and &ofr;&sfr;&ofr; 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(&sfr;&lfr; m | n ) and U(&ofr;&sfr;&pfr; 2|2 n ) do not admit any non-trivial formal deformations of Gerstenhaber type.

0 Bookmarks
·
52 Views
• Source
##### Article: A Hochschild's 6-term exact sequence for restricted Lie superalgebras
[Hide abstract]
ABSTRACT: In [5], Hochschild established a 6-term exact sequence for the cohomology of restricted Lie algebras. We generalize this result to restricted Lie superalgebras.
09/2011;
• Source
##### Article: Generalised Verma modules for the orthosymplectic Lie superalgebra osp(k|2)
[Hide abstract]
ABSTRACT: The composition factors and their multiplicities are determined for generalised Verma modules over the orthosymplectic Lie superalgebra osp(k|2). The results enable us to obtain explicit formulae for the formal characters and dimensions of the finite-dimensional irreducible modules. Applying these results, we also compute the first and second cohomology groups of the Lie superalgebra with coefficients in finite-dimensional Kac modules and irreducible modules.
11/2009;
• Source
##### Article: Generalised Jantzen filtration of Lie superalgebras I
[Hide abstract]
ABSTRACT: A Jantzen type filtration for generalised Varma modules of Lie superalgebras is introduced. In the case of type I Lie superalgebras, it is shown that the generalised Jantzen filtration for any Kac module is the unique Loewy filtration, and the decomposition numbers of the layers of the filtration are determined by the coefficients of inverse Kazhdan-Lusztig polynomials. Furthermore, the length of the Jantzen filtration for any Kac module is determined explicitly in terms of the degree of atypicality of the highest weight. These results are applied to obtain a detailed description of the submodule lattices of Kac modules. Comment: This is the final version to appear in the Journal of European Math Society. LaTeX, 31 pages
01/2010;