Constructing semisimple subalgebras of semisimple Lie algebras

TL;DR

This paper presents algorithms for classifying semisimple subalgebras of semisimple Lie algebras, providing a database of classifications for ranks up to 8 within the GAP4 SLA package.

Contribution

It introduces new algorithms for classification and provides a comprehensive database of semisimple subalgebras for simple Lie algebras up to rank 8.

Findings

Classified semisimple subalgebras of Lie algebras up to rank 8

Developed algorithms implemented in GAP4 SLA package

Provided explicit descriptions and inclusion relations of subalgebras

Abstract

Algorithms are described that help with obtaining a classification of the semisimple subalgebras of a given semisimple Lie algebra, up to linear equivalence. The algorithms have been used to obtain classifications of the semisimple subalgebras of the simple Lie algebras of ranks <= 8. These have been made available as a database inside the SLA package of GAP4. The subalgebras in this database are explicitly given, as well as the inclusion relations among them.