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Subalgebras of the rank two semisimple Lie algebras. (English) Zbl 1398.17005

Summary: In this expository article, we describe the classification of the subalgebras of the rank 2 semisimple Lie algebras. Their semisimple subalgebras are well-known, and in a recent series of papers, we completed the classification of the subalgebras of the classical rank 2 semisimple Lie algebras. Finally, Mayanskiy finished the classification of the subalgebras of the remaining rank 2 semisimple Lie algebra, the exceptional Lie algebra \(G_2\). We identify subalgebras of the classification in terms of a uniform classification scheme of Lie algebras of low dimension. The classification is up to inner automorphism, and the ground field is the complex numbers.

MSC:

17B20 Simple, semisimple, reductive (super)algebras
17B25 Exceptional (super)algebras
17B30 Solvable, nilpotent (super)algebras

Software:

SLA
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

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