Hostname: page-component-586b7cd67f-dlnhk Total loading time: 0 Render date: 2024-11-20T16:15:30.981Z Has data issue: false hasContentIssue false
  • English
  • Français

ON ONE-DIMENSIONAL LEIBNIZ CENTRAL EXTENSIONS OF A FILIFORM LIE ALGEBRA

Part of: General nonassociative rings Lie algebras and Lie superalgebras General commutative ring theory

Published online by Cambridge University Press:  29 July 2011

ISAMIDDIN S. RAKHIMOV  and
MUNTHER A. HASSAN
ISAMIDDIN S. RAKHIMOV*
Affiliation:
Institute for Mathematical Research (INSPEM) Department of Mathematics, FS, Universiti Putra Malaysia, UPM, 43400, Serdang, Selangor Darul Ehsan, Malaysia (email: [email protected])
MUNTHER A. HASSAN
Affiliation:
Institute for Mathematical Research (INSPEM), Serdang, Selangor Darul Ehsan, Malaysia (email: [email protected])
*
✉For correspondence; e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The paper deals with the classification of Leibniz central extensions of a filiform Lie algebra. We choose a basis with respect to which the multiplication table has a simple form. In low-dimensional cases isomorphism classes of the central extensions are given. In the case of parametric families of orbits, invariant functions (orbit functions) are provided.

Keywords

Lie algebrafiliform Leibniz algebraisomorphisminvariant

MSC classification

Secondary: 17A32: Leibniz algebras 17B30: Solvable, nilpotent (super)algebras 13A50: Actions of groups on commutative rings; invariant theory
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 84 , Issue 2 , October 2011 , pp. 205 - 224
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2011

Footnotes

The research was supported by the Grant 01-12-10-978FR MOHE, Malaysia.

References

[1]Albeverio, S., Omirov, B. A. and Rakhimov, I. S., ‘Classification of four-dimensional nilpotent complex Leibniz algebras’, Extracta Math. 21(3) (2006), 197–210.Google Scholar
[2]Gomez, J. R., Jimenez-Merchan, A. and Khakimdjanov, Y., ‘Low-dimensional filiform Lie algebras’, J. Pure Appl. Algebra 130 (1998), 133–158.CrossRefGoogle Scholar
[3]Hakimjanov (Khakimdjanov), You. B., ‘Variété des lois d’algèbres de Lie nilpotentes’, Geom. Dedicata 40 (1991), 229–295.Google Scholar
[4]Loday, J.-L., ‘Une version noncommutative des algèbres de Lie: les algèbres de Leibniz’, Enseign. Math. 39 (1993), 269–293.Google Scholar
[5]Loday, J.-L. and Pirashvili, T., ‘Universal enveloping algebras of Leibniz algebras and (co)homology’, Math. Ann. 296 (1993), 139–158.CrossRefGoogle Scholar
[6]Omirov, B. A. and Rakhimov, I. S., ‘On Lie-like complex filiform Leibniz algebras’, Bull. Aust. Math. Soc. 79 (2009), 391–404.CrossRefGoogle Scholar
[7]Umlauf, K. A., Über die Zusammensetzung der endlichen continuierlichen Transformationsgruppen, insbesondere der Gruppen vom Range Null, Inaugural-Dissertation, Universität Leipzig (Von Breitkopf & Härtel, Leipzig, 1891).Google Scholar