Primitive subalgebras of complex Lie algebras. I: Primitive subalgebras of the classical complex Lie algebras (Q811631)

A proper subalgebra \({\mathcal P}\) of a Lie algebra \({\mathfrak g}\) is called primitive if (1) \({\mathcal P}\) contains no proper ideal of \({\mathfrak g}\) and (2) \({\mathcal P}\) is the maximal invariant subalgebra with respect to the action of \(\text{Int}_{\mathcal P}{\mathfrak g}\), where \(\text{Int}_{\mathcal P}{\mathfrak g}\) is the subgroup of the group of inner automorphisms of the algebra \({\mathfrak g}\), which consists of those automorphisms which keep \({\mathcal P}\) on its place. In the paper all primitive subalgebras of the classical complex Lie algebras are listed.