ABELIAN EXTENSIONS OF SOLVABLE LEIBNIZ ALGEBRA WITH NATURALLY GRADED FILIFORM NILRADICAL OF MAXIMAL CODIMENSION
Using the method of central extensions, we can construct only those Leibniz algebras with nontrivial
centers. Therefore, to identify Leibniz algebras with trivial centers, we apply the method of abelian
extensions. In this paper, we provide a classification of one-dimensional abelian extensions of
solvable Leibniz algebras whose nilradical is a naturally graded filiform Leibniz algebra of maximal
codimension. We give explicit descriptions of these extensions and determine their structures up to
isomorphism.
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