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
[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
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