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Proceedings of the London Mathematical Society Advance Access first published online on November 27, 2006
This version published online on December 5, 2006
Proceedings of the London Mathematical Society, 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

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 osp2|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 slm|n and osp2|2n do not admit any non-trivial formal deformations of Gerstenhaber type.


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