On certain classes of Lie algebras (Q1204644)

Earlier the author introduced an important class of varieties of Lie algebras, so called varieties of API-algebras, for which an analogue of A. Shirshov's Height Theorem holds. Here he shows that the definition of the class, in terms of identical relations of complicated form, can be replaced by a more elegant one, in terms of the Young diagrams involved in the decomposition of multilinear non-identities: there exists an \(n\) such that all diagrams containing a rectangle with diagonal of length \(\geq n\) vanish on the varieties in question.