Geodesic
On Flags and Maximal Chains of Lower Modular Subalgebras of Lie Algebras
Kevin Bowman1 ; David A. Towers2 ; Vicente R. Varea3, 4
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
4[
Journal of Lie Theory, Tome 17 (2007) no. 3, pp. 605-616

Voir la notice de l'article provenant de la source Heldermann Verlag

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.
Classification : 17B05, 17B50, 17B30, 17B20
Mots-clés : 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 , 4

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
4 [ 
Kevin Bowman; David A. Towers; Vicente R. Varea. On Flags and Maximal Chains of Lower Modular Subalgebras of Lie Algebras. Journal of Lie Theory, Tome 17 (2007) no. 3, pp. 605-616. http://geodesic.mathdoc.fr/item/JOLT_2007_17_3_a10/
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     author = {Kevin Bowman and David A. Towers and Vicente 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},
     url = {http://geodesic.mathdoc.fr/item/JOLT_2007_17_3_a10/}
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