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 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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Abstract In this paper we give the description of some non-strongly nilpotent Leibniz algebras. We pay our attention to the subclass of nilpotent Leibniz algebras, which is called filiform. Note that the set of filiform Leibniz algebras of fixed dimension can be decomposed into three disjoint families. We describe the pre-derivations of filiform Leibniz algebras for the first and second families and determine those algebras in the first two classes of filiform Leibniz algebras that are non-strongly nilpotent.
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