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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.

MSC:
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
Software:
SLA
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References:
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