On Flags And Maximal Chains Of Lower Modular Subalgebras Of Lie Algebras.

Bowman, Kevin and Towers, David A. and Varea, Vicente R. (2007) On Flags And Maximal Chains Of Lower Modular Subalgebras Of Lie Algebras. Journal of Lie Theory, 17 (3). pp. 605-616.

Abstract

In this paper we study the class ${\cal F}$ of Lie algebras having a flag of subalgebras, and the class ${\cal Ch}_{lm}$ of Lie algebras having a maximal chain of lower modular subalgebras. We show that ${\cal F} \subseteq {\cal Ch}_{lm}$ and that both are extensible formations that are subalgebra closed. We derive a number of properties relating to these two classes, including a classification of the algebras in each class over a field of characteristic zero.