Abstract
We consider the connected integer gradations on a type of n dimensional nilpotent Lie algebras. We study the case where the number of non trivial subspaces is n - 1 for those gradations, when the nilindex of the algebras is n - 2 (quasi-filiform Lie algebras). We show how Symbolic Calculus can be useful to obtain the classification of such a family of graded algebras, which is determined for n ≤ 15.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
F. Bratzlavsky. Sur les algèbres Admettant un Tore de d‘Automoorphismes Donné. Journal of Algebra 30 (1974) 305–316.
J. M. Cabezas, J. R. Gomez, Jimenez-Merchan. Family of p-filiform Lie algebras in Algebra and Operator Theory. Kluwer Academics Publishers (1998) 93–102.
R. Carles Sur certaines classes d’algèbres de Lie rigides in Mathematische Annalen. Springer-Verlag (1985) 477–488.
J. R. Gómez, A. Jimenéz-Merchán. The graded algebras of a class of Lie algebras in Mathematics with Vision. Computational Mechanics Publications (1995) 151–158.
J. R. Gomez, A. Jimenéz-Merchán, J. Reyes. Filiform Lie Algebras of maximun Length. Extracta Mathematicae (to appear).
J. R. Gomez, A. Jimenéz-Merchán, J. Reyes. Quasi-Filiform Lie Algebras of Maximum Length. Linear Algebra and its Applications (to appear).
M. Goze, Y. Khakimdjanov. Sur les algèbres de Lie nilpotentes admettant un tore de dérivations. Manuscripta Mathematica 84 (1994) 115–224.
M. Goze, Y. Khakimdjanov Nilpotent Lie algebras. Kluwer A. P. (1996).
Y. Khakimdjanov. Variétés des lois d’algébres de Lie nilpotentes. Geometria Dedicata 40, 3 (1991) 269–295.
J. Reyes Algebras de Lie Casifiliforme Graduadas de Longitud Maximal. Ph.D. Thesis. Sevilla (1998).
M. Vergne. Cohomologie des algèbres de Lie nilpotentes. Application à l’étude de la variété des algèbres de Lie nilpotentes. Bulletin Société Mathematique de la France 98 (1970) 81–116.
S. Wolfram The Mathematica Book, 4th. ed. Cambrige University Press (1999).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Gómez, J.R., Jiménez-Merchán, A., Reyes, J. (2001). Low-Dimensional Quasi-Filiform Lie Algebras with Great Length. In: Ganzha, V.G., Mayr, E.W., Vorozhtsov, E.V. (eds) Computer Algebra in Scientific Computing CASC 2001. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-56666-0_20
Download citation
DOI: https://doi.org/10.1007/978-3-642-56666-0_20
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-62684-5
Online ISBN: 978-3-642-56666-0
eBook Packages: Springer Book Archive