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Constructing semisimple subalgebras of semisimple Lie algebras. (English) Zbl 1255.17007

Summary: 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 \(\leq 8\). 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.

MSC:

17B20 Simple, semisimple, reductive (super)algebras
17B25 Exceptional (super)algebras
17-08 Computational methods for problems pertaining to nonassociative rings and algebras

Software:

SLA; GAP
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Full Text: DOI arXiv

References:

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