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Proceedings of the London Mathematical Society Advance Access originally published online on November 27, 2006
Proceedings of the London Mathematical Society 2007 94(1):91-136; doi:10.1112/plms/pdl005
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© 2006 London Mathematical Society

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

Yucai Su1,2 and R. B. Zhang3

1 Department of Mathematics
University of Science and Technology of China
Hefei 230026
China
2 School of Mathematics and Statistics
University of Sydney
NSW 2006
Australia
ycsu{at}ustc.edu.cn
3 School of Mathematics and Statistics
University of Sydney
NSW 2006
Australia
rzhang{at}maths.usyd.edu.au

Received 12 March 2004. Revision received 8 March 2006.

We explicitly compute the first and second cohomology groups of the classical Lie superalgebras slm|n and oso 2|2n 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(slm|n) and U(osp2|2n) do not admit any non-trivial formal deformations of Gerstenhaber type.


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