Pre-derivations and description of non-strongly nilpotent filiform Leibniz algebras
Kobiljon AbdurasulovV.I. Romanovsky Institute of Mathematics, Academy of Sciences of Uzbekistan , Tashkent , , UzbekistanAbror KhudoyberdiyevNational University of Uzbekistan , Tashkent , , V.I. Romanovsky Institute of Mathematics, Academy of Sciences of Uzbekistan , Tashkent , , UzbekistanM. LadraDepartment of Mathematics, Institute of Mathematics, Campus Vida , University of Santiago de Compostela , , SpainAloberdi SattarovV.I. Romanovsky Institute of Mathematics, Academy of Sciences of Uzbekistan , Tashkent , , Uzbekistan
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Аннотация
In this paper we investigate pre-derivations of filiform Leibniz algebras. Recall that the set of filiform Leibniz algebras of fixed dimension can be decomposed into three non-intersected families. We describe the pre-derivation of filiform Leibniz algebras for the first and second families. We found sufficient conditions under which filiform Leibniz algebras are strongly nilpotent. Moreover, for the first and second families, we give the description of characteristically nilpotent algebras which are non-strongly nilpotent.
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