Subalgebras of the rank two semisimple Lie algebras

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 . 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.

KEYWORDS:

• Semisimple Lie algebras
• solvable Lie algebras
• Levi decomposable algebras
• Lie subalgebras

AMS SUBJECT CLASSIFICATIONS:

• 17B05
• 17B10
• 17B20
• 17B25
• 17B30

Acknowledgements

We also greatly thank Matthew Wu who checked our computations in the case.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The work of A.D. is partially supported by a research grant from the Professional Staff Congress/City University of New York [grant number TRADA-47-36]. The work of J.R. is partially supported by the Natural Sciences and Engineering Research Council [grant number 3166-09].