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Journal of Lie Theory 17 (2007), No. 3, 605--616
Copyright 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


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

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