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June 2020 The second cohomology groups of nilpotent orbits in classical Lie algebras
Indranil Biswas, Pralay Chatterjee, Chandan Maity
Kyoto J. Math. 60(2): 717-799 (June 2020). DOI: 10.1215/21562261-2019-0046

Abstract

The second de Rham cohomology groups of nilpotent orbits in noncompact real forms of classical complex simple Lie algebras are explicitly computed. Furthermore, the first de Rham cohomology groups of nilpotent orbits in noncompact classical simple Lie algebras are computed, and we prove them 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. "The second cohomology groups of nilpotent orbits in classical Lie algebras." Kyoto J. Math. 60 (2) 717 - 799, June 2020. https://doi.org/10.1215/21562261-2019-0046

Information

Received: 5 September 2017; Accepted: 9 January 2018; Published: June 2020
First available in Project Euclid: 13 March 2020

zbMATH: 07223248
MathSciNet: MR4094747
Digital Object Identifier: 10.1215/21562261-2019-0046

Subjects:
Primary: 57T15
Secondary: 17B08

Rights: Copyright © 2020 Kyoto University

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Vol.60 • No. 2 • June 2020
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