David Towers: Solvable Lie A-algebras
From CRCG-Wiki
A finite-dimensional Lie algebra is called an A-algebra if all of its nilpotent subalgebras are abelian. These arise in the study of constant Yang-Mills potentials and have also been particularly important in relation to the problem of describing residually finite varieties. Our purpose is to obtain structural results on solvable A-algebras. In particular, they split over each term in their derived series. This leads to a decomposition of the algebra to which the ideals relate nicely. When the algebra is completely solvable we can locate the position of the maximal nilpotent subalgebras. More detailed structure results can be given when the underlying field is algebraically closed.
