Levi decomposable algebras in the classical Lie algebras

We examine embeddings of an important class of Levi decomposable algebras into the classical Lie algebras. In particular, we classify the embeddings of AnCn+1AnCn+1, BnC2n+1BnC2n+1, CnC2nCnC2n, and DnC2nDnC2n into the complex simple Lie algebras An+1An+1, Bn+1Bn+1, Cn+1Cn+1, and Dn+1Dn+1, respectively, up to inner automorphism.