Abstract
This paper, an approach to the classification of nilpotent Lie algebras g of any dimension with a Goze’s invariant (dimg — p, 1,…, 1), provides an explicit classification for p ≥ dimg — 3.
This work has been partially sponsored by the PAICYT project from the Government / Council of Andalucía.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
J.M. Ancochea, M. Goze, Classification des algèbres de Lie filiformes de dimension 8, Archiv. Math., 50(1988), 511–525
J.M. Ancochea, M. Goze, Classification des algèbres de Lie nilpotentes de dimension 7, Archiv. Math., 52(1989), 175–185
L. Boza, F.J. Echarte, J. Núñnez. Classification of complex filiform Lie algebras of dimension 10, Algebra, Groups and Geometries, 11:3(1994), 253–276
J. Dixmier, Sur les reprèsentations unitaires des groupes de Lie nilpotentes III, Canadian J. Math., 10(1958), 321–348
J.R. Gómez, F.J. Echarte, Classification of complex filiform nilpotent Lie algebras of dimension 9, Rendiconti Cagliari, 61:1(1991), 21–29
J.R. Gómez, M. Goze, Y. Khakimdjanov, On the k-abelian filiform Lie algebras, Communications in algebra, 25:2(1997), 431–450
J.R. Gómez, A. Jiménez-Merchân, Y. Khakimdjanov, Low-Dimensional Filiform Lie Algebras, to appear in Journal of Pure and Applied Algebra.
V.V. Morosov, Clasification of nilpotent Lie algebras, (in Russian) Isvestia Vys Ucheb. Zay. 4(1958), 161–171
M. Vergne, Cohomologie des algèbres de Lie nilpotentes. Application à l’étude de la varieté des algèbres de Lie nilpotentes, Bull. Soc. Math. France, 98(1970), 81–116
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1998 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Cabezas, J.M., Gómez, J.R., Jimenez-Merchán, A. (1998). Family of p-Filiform Lie Algebras. In: Khakimdjanov, Y., Goze, M., Ayupov, S.A. (eds) Algebra and Operator Theory. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5072-9_7
Download citation
DOI: https://doi.org/10.1007/978-94-011-5072-9_7
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-6130-8
Online ISBN: 978-94-011-5072-9
eBook Packages: Springer Book Archive