Journal Home Page Cumulative Index List of all Volumes Complete Contentsof this Volume Previous Article Journal of Lie Theory 17 (2007), No. 3, 605--616Copyright Heldermann Verlag 2007 On Flags and Maximal Chains of Lower Modular Subalgebras of Lie Algebras Kevin Bowman Dept. of Physics, Astronomy and Mathematics, University of Central Lancashire, Preston PR1 2HE, England David A. Towers Dept. of Mathematics, Lancaster University, Lancaster LA1 4YF, England Vicente R. Varea Dept. of Mathematics, University of Zaragoza, Zaragoza 50009, Spain [Abstract-pdf] We study the class ${\cal F}$ of Lie algebras having a flag of subalgebras, and the class ${\cal C}\hskip-1pt {\it h}_{lm}$ of Lie algebras having a maximal chain of lower modular subalgebras. We show that ${\cal F} \subseteq {\cal C}\hskip-1pt{\it h}_{lm}$ 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. Keywords: Lie algebras, flags of subalgebras, maximal chains of subalgebras, lower modular subalgebras, quasi-ideals. MSC: 17B05, 17B50, 17B30, 17B20 [ Fulltext-pdf  (170  KB)] for subscribers only.