Solvable Lie algebras with quasifiliform nilradicals. (English) Zbl 1230.17007
Summary: All finite-dimensional indecomposable solvable Lie algebras \(\mathfrak g\), having the quasifiliform Lie algebra \(\overline N\) as the nilradical, are constructed and classified. It turns out that the dimension of \(\mathfrak g\) is at most \(\dim\,\overline N +3\).
MSC:
17B30 | Solvable, nilpotent (super)algebras |
17B40 | Automorphisms, derivations, other operators for Lie algebras and super algebras |
17B70 | Graded Lie (super)algebras |
References:
[1] | Cartan E., (Paris: thesis, Nony). Oeuvres Completes, Partie I. Tome 1 pp 137– (1894) |
[2] | DOI: 10.1080/10586458.2005.10128911 · Zbl 1173.17300 · doi:10.1080/10586458.2005.10128911 |
[3] | Gantmacher , F. ( 1939 ).Rec. Math. (Mat. Sbornik) N.S.5 : 217 – 250 . |
[4] | Goze M., Nilpotent Lie Algebras (1996) · Zbl 0845.17012 |
[5] | Jacobson N., Lie Algebras (1979) |
[6] | Levi E. E., Atti Accad. Sci. Torino 40 pp 551– (1905) |
[7] | DOI: 10.1088/0305-4470/27/2/024 · Zbl 0828.17009 · doi:10.1088/0305-4470/27/2/024 |
[8] | DOI: 10.1016/0024-3795(90)90251-7 · Zbl 0718.17010 · doi:10.1016/0024-3795(90)90251-7 |
[9] | DOI: 10.1088/0305-4470/26/5/031 · Zbl 0773.17004 · doi:10.1088/0305-4470/26/5/031 |
[10] | DOI: 10.1088/0305-4470/38/12/011 · Zbl 1063.22023 · doi:10.1088/0305-4470/38/12/011 |
[11] | DOI: 10.1088/0305-4470/31/2/033 · Zbl 1001.17011 · doi:10.1088/0305-4470/31/2/033 |
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