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