Classification of seven-dimensional solvable Lie algebras with five-dimensional abelian nilradicaly
DOI:
https://doi.org/10.33043/ANN477M298Abstract
This paper provides a classification of seven-dimensional indecomposable solvable Lie algebras over the real numbers for which the nilradical is five-dimensional and abelian. We follow a technique that was first introduced by Mubarakzyanov.
References
E.Cartan. Sur la Reduction a sa Forme Canonique de la Structure d’un Groupe de Transformations Fini et Continu. Amer. J. Math., 18(1):1–61, 1896.
Felix Gantmacher. On the classification of real simple Lie groups. Rec. Math. [Mat. Sbornik] N.S., 5 (47):217-250, 1939.
M. Gong. Classification of Nilpotent Lie Algebras of Dimension 7 ( Over Algebraically Closed Fields and R). PhD thesis, University of Waterloo, 1998.
Sigurdur Helgason. Differential geometry, Lie groups, and symmetric spaces, volume 80 of Pure and Applied Mathematics. Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1978.
F. Hindeleh and G. Thompson. Seven dimensional Lie algebras with a fourdimensional nilradical. Algebras Groups Geom., 25(3):243-265, 2008.
James E. Humphreys. Introduction to Lie algebras and representation theory, volume 9 of Graduate Texts in Mathematics. Springer-Verlag, New York-Berlin, 1978. Second printing, revised.
Nathan Jacobson. Lie algebras. Interscience Tracts in Pure and Applied Mathematics, No. 10. Interscience Publishers (a division of John Wiley Sons), New York-London, 1962.
Vu A. Le, Tuan A. Nguyen, Tu T. C. Nguyen, Tuyen T. M. Nguyen, and Thieu N. Vo. Classification of 7-dimensional solvable lie algebras having 5-dimensional nilradicals, 2021.
V. V. Morozov. Classification of nilpotent lie algebras of sixth order. Izv. Vysš. Uˇcebn. Zaved. Matematika, 1958(4(5)):161-171, 1958.
G. M. Mubarakzjanov. Certain theorems on solvable Lie algebras. Izv. Vysš. Uˇcebn. Zaved. Matematika, 1966(6(55)):95-98, 1966.
G. M. Mubarakzjanov. Classification of real structures of lie algebras of fifth order. Izv. Vysshikh Uchebn. Zavedenii Mat., 3(34):99-106, 1964
G. M. Mubarakzjanov. Classification of solvable lie algebras of sixth order with a non-nilpotent basis element. Izv. Vysshikh Uchebn. Zavedenii Mat., 4(35):104-116, 1963.
G. M. Mubarakzjanov. On solvable lie algebras. Izv. Vysshikh Uchebn. Zavedenii Mat., 1(32):114-123, 1963.
Jean-Claude Ndogmo. Sur les fonctions invariantes sous l’action coadjointe d’une algebre de Lie resoluble avec nilradical abelien. ProQuestLLC, Ann Arbor, MI, 1994. Thesis (Ph.D.)–Universite de Montreal (Canada).
J. C. Ndogmo and P. Winternitz. Solvable Lie algebras with abelian nilradicals. J. Phys. A, 27(2):405–423, 1994.
Alan Parry. A Classification of real indecomposable solvable Lie algebras of small dimension with codimension one nilradical. 2007. Thesis (M.Sc.)–Utah State University.
J. Patera, R.T. Sharp, P. Winternitz, and H. Zassenhaus. Invariants of real low dimension lie algebras. J. Math. Phys., 17:986–994, 1976.
Craig Seeley. 7-dimensional nilpotent Lie algebras. Trans. Amer. Math. Soc., 335(2):479–496, 1993.
Anastasia Shabanskaya. Classification of six dimensional solvable indecomposable Lie algebras with a codimension one nilradical over R. ProQuestLLC, Ann Arbor, MI, 2011. Thesis(Ph.D.)–The University of Toledo.
Anastasia Shabanskaya and Gerard Thompson. Six-dimensional Lie algebras with a five-dimensional nilradical. J. Lie Theory, 23(2):313–355, 2013.
P. Turkowski. Solvable lie algebras of dimension six. J. Math. Phys., 31(6):1344–1350, 1990.
K. A. Umlauf. Über die Zusammensetzung der endlichen continuierliche Transformation gruppen insbesondere der Gruppen von Rang null. 1891. Thesis(Ph.D.)–University of Leipzig.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2026 Jacksyn Bakeberg, Kaite Blaine, Firas Hindeleh
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
