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arXiv · 1705.03600

Subalgebras of the rank two semisimple Lie algebras

Andrew Douglas·Joe Repka
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Abstract

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.

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Andrew Douglas, Joe Repka. 2017-05-10. Subalgebras of the rank two semisimple Lie algebras. https://arxiv.org/abs/1705.03600

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