I am interested about the last results belong to the classification of the low dimensional Leibniz algebra. Does anybody can help me?
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$\begingroup$ I found some papers related to the classification of nil potent Lie Algebras, I think should be some connection between this two classifications. Because the results of Rakhimov and Langari are based on the same methods of Skjelbred and Sund. What is your opinion regarding this matter? $\endgroup$– AnvarCommented May 6, 2010 at 10:34
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3 Answers
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Two more papers by Albeverio, S., Omirov, B.A., Rakhimov, Isamiddin S.:
Varieties of nilpotent complex Leibniz algebras of dimensions less then five, Comm. Algebra 33 (2005), N5, 1575-1585 DOI:10.1081/AGB-200061038
Classification of 4-dimensional nilpotent complex Leibniz algebras, Extr. Math. 21 (2006), No. 3, 197-210 http://www.unex.es/extracta/Vol-21-3/21J3Albe.pdf (also arXiv:math/0611831)
There are probably some other papers on the subject by Ayupov, Omirov, and their collaborators.
answered May 13, 2010 at 6:15
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I think that only the three-dimensional nilpotent Leibniz algebras have been classified. There is a recent paper (PDF link) by Rakhimov and Langari where this is done.
answered May 6, 2010 at 10:23
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Rakhimov and Hassan have given a complete classification of a subclass of complex filiform Leibniz algebras in dimensions 5 and 6 in http://ftp.fi.muni.cz/mount/muni.cz/EMIS/journals/2008-09-12b.pdf.
