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ON LIE-LIKE COMPLEX FILIFORM LEIBNIZ ALGEBRAS

Part of: General nonassociative rings Lie algebras and Lie superalgebras

Published online by Cambridge University Press:  14 May 2009

B. A. OMIROV  and
I. S. RAKHIMOV
B. A. OMIROV*
Affiliation:
Institute of Mathematics, Uzbekistan Academy of Science, F. Hodjaev str. 29, 100125 Tashkent, Uzbekistan (email: omirovb@mail.ru)
I. S. RAKHIMOV
Affiliation:
Institute for Mathematical Research (INSPEM), Department of Mathematics, Universiti Putra Malaysia, Faculty of Science, 43400 UPM Serdang, Selangor Darul Ehsan, Malaysia (email: isamiddin@science.upm.edu.my, risamiddin@mail.ru)
*
✉For correspondence; e-mail: omirovb@mail.ru
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Abstract

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In this paper we propose an approach to classifying a subclass of filiform Leibniz algebras. This subclass arises from the naturally graded filiform Lie algebras. We reconcile and simplify the structure constants of such a class. In the arbitrary fixed dimension case an effective algorithm to control the behavior of the structure constants under adapted transformations of basis is presented. In one particular case, the precise formulas for less than 10 dimensions are given. We provide a computer program in Maple that can be used in computations as well.

Keywords

Lie algebrafiliform Leibniz algebranatural gradationisomorphism criterion

MSC classification

Secondary: 17A32: Leibniz algebras 17B30: Solvable, nilpotent (super)algebras 17B70: Graded Lie (super)algebras
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 79 , Issue 3 , June 2009 , pp. 391 - 404
Copyright
Copyright © Australian Mathematical Society 2009

Footnotes

This work was supported by the Science Fund Grant Project 06-01-04-SF0122 MOSTI (Malaysia).

References

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