ANALOGUES OF THE FRATTINI SUBALGEBRA

Abstract

For a Lie algebra, L, the Frattini subalgebra F(L) is the intersection of all maximal subalgebras of L. We develop two analogues of the Frattini subalgebra, namely nF rat(L) and R(L). Specifically, we develop properties involving non-generators, containment relations, and nilpotency.