Real forms of embeddings of maximal reductive subalgebras of the complex simple Lie algebras of rank up to 8

TL;DR

This paper provides comprehensive tables of noncompact real forms of maximal reductive subalgebras for complex simple Lie algebras up to rank 8, using computational methods and discussing applications in physics.

Contribution

It offers the first systematic classification of these real forms for Lie algebras of rank up to 8, with computational techniques and physical applications.

Findings

Tables of noncompact real forms of subalgebras are provided.

Computational methods were used to obtain the classifications.

Applications in theoretical physics are discussed.

Abstract

We give tables of noncompact real forms of maximal reductive subalgebras of complex simple Lie algebras of rank up to 8. These were obtained by computational methods that we briefly describe. We also discuss applications in theoretical physics of these embeddings.