On filiform Leibniz algebras of dimension nine.

The paper is devoted to classification problem of a subclass of filiform Leibniz algebras, obtained from naturally graded non-Lie filiform Leibniz algebra. In the paper “On isomorphisms and invariants of finite dimensional complex filiform Leibniz algebras”, by I.S. Rakhimov and U.D. Bekbaev, Communications in Algebra (appears) it was suggested an approach for the isomorphism problem of this class in terms of invariants. This paper is an application of the results of the above work to a subclass of 9-dimensional filiform Leibniz algebras. Here we give a complete classification and as a result one obtains 23 continuous families and 12 isolated classes of algebras. Invariant functions for the continuous families of algebras cases are listed, while representatives for the isolated once are provided.

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