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

Abstract

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 The motivation to write this paper is an unpublished yet result of J.R.Gomez, B.A.Omirov on necessary and sufficient conditions for two finite dimensional complex filiform Leibniz algebras to be isomorphic.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.

arXiv comment14 pages

References in corpus (1)

• On classification of complex filiform Leibniz algebras

Cited by in corpus (4)

• On low-dimensional filiform Leibniz algebras and their invariants
• On Isomorphism Classes and Invariants of Low Dimensional Complex Filiform Leibniz Algebras (PART 1)
• On one dimensional Leibniz central extensions of a naturally graded filiform Lie algebra
• On Description of Isomorphism Classes of filiform Leibniz algebras in dimensions 7 and 8