Abstract
In this work, we consider extensions of solvable Lie algebras with naturally graded filiform nilradicals. Note that there exist two naturally graded filiform Lie algebras [Formula: see text] and [Formula: see text] We find all one-dimensional extensions of solvable Lie algebras with nilradical [Formula: see text]. We prove that there exists a unique non-split central extension of solvable Lie algebras with nilradical [Formula: see text] of maximal codimension. Moreover, all one-dimensional extensions of solvable Lie algebras with nilradical [Formula: see text] whose codimension is equal to one are found and we compared these solvable algebras with the solvable algebras with nilradicals that are one-dimensional central extension of algebra [Formula: see text].
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