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Levi decomposable algebras in the classical Lie algebras. (English) Zbl 1354.17007
Summary: We examine embeddings of an important class of Levi decomposable algebras into the classical Lie algebras. In particular, we classify the embeddings of \(A_n\uplus \mathbb{C}^{n + 1}\), \(B_n\uplus \mathbb{C}^{2 n + 1}\), \(C_n\uplus \mathbb{C}^{2 n}\), and \(D_n\uplus \mathbb{C}^{2 n}\) into the complex simple Lie algebras \(A_{n + 1}\), \(B_{n + 1}\), \(C_{n + 1}\), and \(D_{n + 1}\), respectively, up to inner automorphism.

MSC:
17B20 Simple, semisimple, reductive (super)algebras
17B40 Automorphisms, derivations, other operators for Lie algebras and super algebras
Software:
SLA; GAP
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References:
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