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arXiv · 1611.08369

The second cohomology groups of nilpotent orbits in classical Lie algebras

Indranil Biswas·Pralay Chatterjee·Chandan Maity
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Abstract

The second de Rham cohomology groups of nilpotent orbits in non-compact real forms of classical complex simple Lie algebras are explicitly computed. Furthermore, the first de Rham cohomology groups of nilpotent orbits in non-compact classical simple Lie algebras are computed; they are proven to be zero for nilpotent orbits in all the complex simple Lie algebras. A key component in these computations is a description of the second and first cohomology groups of homogeneous spaces of general connected Lie groups which is obtained here. This description, which generalizes a previous theorem of the first two authors, may be of independent interest.

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Indranil Biswas, Pralay Chatterjee, Chandan Maity. 2022-03-27. The second cohomology groups of nilpotent orbits in classical Lie algebras. https://doi.org/10.1215/21562261-2019-0046

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