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

Part of: Lie algebras and Lie superalgebras General nonassociative rings 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: risamiddin@gmail.com)
MUNTHER A. HASSAN
Affiliation:
Institute for Mathematical Research (INSPEM), Serdang, Selangor Darul Ehsan, Malaysia (email: munther_abd@yahoo.com)
*
✉For correspondence; e-mail: risamiddin@gmail.com
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Abstract

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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

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