Algebra Seminar

The Ado-Iwasawa Theorem asserts that a finite-dimensional Lie algebra has a faithful finite-dimensional module. I strengthen that result. Let F be a saturated formation of soluble Lie algebras. Let S in F be an ideal of the finite-dimensional Lie algebra L. I show that there exists a faithful finite-dimensional L-module which, as S-module, is F-hypercentral.

Taking the special case of the formation of supersoluble algebras, this gives the existence of a representation of L in which the supersoluble ideal S of L is represented by upper triangular matrices.