On the second cohomology of nilpotent orbits in exceptional Lie algebras

TL;DR

This paper computes the second cohomology dimensions of nilpotent orbits in non-compact exceptional Lie algebras, providing exact values for most cases and bounds for others, advancing understanding of their cohomological properties.

Contribution

It offers new calculations and bounds for the second cohomology groups of nilpotent orbits in exceptional Lie algebras, filling gaps in existing knowledge.

Findings

Exact second cohomology dimensions for most nilpotent orbits

Upper bounds for remaining nilpotent orbit cases

Enhanced understanding of cohomological structure in exceptional Lie algebras

Abstract

In this paper we consider non-compact non-complex exceptional Lie algebras, and compute the dimensions of the second cohomology groups for most of the nilpotent orbits. For the rest of cases of nilpotent orbits, which are not covered in the above computations, we obtain upper bounds for the dimensions of the second cohomology groups.