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The subalgebras of \(A_2\). (English) Zbl 1377.17007
The paper provides a classification of all nonsemisimple subalgebras of the Lie algebra of traceless matrices or order \(3\) with complex entries, denoted by \(A_2\). In order to do this, the authors classify the solvable and Levi decomposable subalgebras of \(A_2\). By using the well known classification of semisimple subalgebras and the Levi’s Theorem, it leads to the classification of all subalgebras of \(A_2\). The classification is up to inner automorphism.

17B05 Structure theory for Lie algebras and superalgebras
17B10 Representations of Lie algebras and Lie superalgebras, algebraic theory (weights)
17B20 Simple, semisimple, reductive (super)algebras
17B30 Solvable, nilpotent (super)algebras
Full Text: DOI
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