Gradings on classical central simple real Lie algebras

TL;DR

This paper classifies all possible gradings by abelian groups on classical central simple real Lie algebras, excluding type D4, providing a comprehensive understanding of their structural gradings over real fields.

Contribution

It offers a complete classification of G-gradings on classical central simple real Lie algebras, extending previous work to include all types except D4.

Findings

Complete classification of G-gradings on classical central simple real Lie algebras

Excludes type D4 due to complexity

Results applicable over real closed fields

Abstract

For any abelian group $G$, we classify up to isomorphism all $G$-gradings on the classical central simple Lie algebras, except those of type $D_4$, over the field of real numbers (or any real closed field).