Journal of Lie Theory

no. 3
On Flags and Maximal Chains of Lower Modular Subalgebras of Lie Algebras
Kevin Bowman1; David A. Towers2; Vicente R. Varea3
1Dept. of Physics, Astronomy and Mathematics, University of Central Lancashire, Preston PR1 2HE, England
2Dept. of Mathematics, Lancaster University, Lancaster LA1 4YF, England
3Dept. of Mathematics, University of Zaragoza, Zaragoza 50009, Spain
Journal of Lie Theory, Volume 17 (2007) no. 3, pp. 605-616
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.
DOI: 10.5802/jolt.465
Classification: 17B05, 17B50, 17B30, 17B20
Keywords: Lie algebras, flags of subalgebras, maximal chains of subalgebras, lower modular subalgebras, quasi-ideals

Kevin Bowman  1 ; David A. Towers  2 ; Vicente R. Varea  3

1 Dept. of Physics, Astronomy and Mathematics, University of Central Lancashire, Preston PR1 2HE, England
2 Dept. of Mathematics, Lancaster University, Lancaster LA1 4YF, England
3 Dept. of Mathematics, University of Zaragoza, Zaragoza 50009, Spain 
Kevin Bowman; David A. Towers; Vicente R. Varea. On Flags and Maximal Chains of Lower Modular Subalgebras of Lie Algebras. Journal of Lie Theory, Volume 17 (2007) no. 3, pp. 605-616. doi: 10.5802/jolt.465
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     title = {On {Flags} and {Maximal} {Chains} of {Lower} {Modular} {Subalgebras} of {Lie} {Algebras}},
     journal = {Journal of Lie Theory},
     pages = {605--616},
     year = {2007},
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     number = {3},
     doi = {10.5802/jolt.465},
     zbl = {1161.17009},
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