Constructing semisimple subalgebras of semisimple Lie algebras

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.