Journal of Lie Theory

no. 3
On Flags and Maximal Chains of Lower Modular Subalgebras of Lie Algebras
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 
@article{JOLT_2007_17_3_a10,
     author = {K. Bowman and D. A. Towers and V. R. Varea},
     title = {On {Flags} and {Maximal} {Chains} of {Lower} {Modular} {Subalgebras} of {Lie} {Algebras}},
     journal = {Journal of Lie Theory},
     pages = {605--616},
     year = {2007},
     volume = {17},
     number = {3},
     doi = {10.5802/jolt.465},
     zbl = {1161.17009},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.465/}
}
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K. Bowman; D. A. Towers; V. 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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