Cohomology of Lie superalgebras Slm|n and Osp2|2n

University of Science and Technology of China, Luchow, Anhui Sheng, China
Proceedings of the London Mathematical Society (Impact Factor: 1.11). 11/2006; 94(1). DOI: 10.1112/plms/pdl005
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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.

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Available from: Yucai Su, Sep 14, 2015
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    • "Comparing with abundant works and results for various cohomology theory of Lie superalgebras (see [1] [6] [8] [10] and references therein), the knowledge about the cohomology theory of restricted Lie superalgebras is poor. To the author's best knowledge, there has not been any serious study in the direction, perhaps because even for simple Lie superalgebras over C their cohomology theory is already very difficult. "
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