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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.
In this paper we investigate the derivations of filiform Leibniz algebras. Recall that the set of filiform Leibniz algebras of fixed dimension is decomposed into three non-intersected families. We found sufficient conditions under which filiform Leib
In this paper we describe central extensions of some nilpotent Leibniz algebras. Namely, central extensions of the Leibniz algebra with maximal index of nilpotency are classified. Moreover, non-split central extensions of naturally graded filiform no
The descriptions (up to isomorphism) of naturally graded $p$-filiform Leibniz algebras and $p$-filiform ($pleq 3$) Leibniz algebras of maximum length are known. In this paper we study the gradation of maximum length for $p$-filiform Leibniz algebras.
This work completes the study of the solvable Leibniz algebras, more precisely, it completes the classification of the $3$-filiform Leibniz algebras of maximum length cite{3-filiform}. Moreover, due to the good structure of the algebras of maximum le
In this paper we investigate Leibniz algebras whose quotient Lie algebra is a naturally graded filiform Lie algebra $n_{n,1}.$ We introduce a Fock module for the algebra $n_{n,1}$ and provide classification of Leibniz algebras $L$ whose corresponding