Lie algebras whose proper subalgebras are either semisimple, abelian or almost-abelian
The author first considers Lie algebras \(L\) having an element \(x\) such that \(C_ L (x)\) is abelian and \(\dim N_ L (C_ L (x))/ C_ L (x)\leq 1\). He also studies the structure of nonsolvable Lie algebras all of whose proper subalgebras are either semisimple, abelian, or almost abelian. He then uses these results in a study of upper semi-modular and relatively complemented Lie algebras. He also obtains information on the structure of Lie algebras which are simple and minimal non-modular, and he determines the Lie algebras with a subalgebra lattice of length 3.
scientific article; zbMATH DE number 681271