The second cohomology groups of nilpotent orbits in classical Lie algebras

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.

65 pages, Final version

References in corpus (3)

• Cohomology of the minimal nilpotent orbit
• On the second cohomology of nilpotent orbits in exceptional Lie algebras
• The Torus-Equivariant Cohomology of Nilpotent Orbits

Cited by in corpus (1)

• Reality of Unipotent elements in Classical Lie Groups