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

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Journal publication date 2007 Journal of Lie Theory 3 17 12 605-616 Published English

### 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.