On Classification of Finite Dimensional Complex Filiform Leibniz Algebras (PartI)

Details On Classification of Finite Dimensional Complex Filiform Leibniz Algebras (PartI) On Classification of Finite Dimensional Complex Filiform Leibniz Algebras (PartI)

2006-12-28

arxiv.org/abs/math/0612805v1

Mathematics

Rings and Algebras

14 pages

Scientific paper

The paper is devoted to classification problem of finite dimensional complex none Lie filiform Leibniz algebras. The motivation to write this paper is an unpublished yet result of J.R.Gomez, B.A.Omirov on necessary and sufficient conditions for two finite dimensional complex filiform Leibniz algebras to be isomorphic. We suggest another approach to this problem. The approach that we use for classification is in terms of invariants. In fact, utilizing this method for any given low dimensional case all filiform Leibniz algebras can be classified. Moreover, the results can be used for geometrical classification of orbits of such algebras. Key-Words: filiform Leibniz algebra, invariant, function, isomorphism.

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