Extensions of solvable Lie algebras with naturally graded filiform nilradical
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Published:2023-05-05
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Volume:
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ISSN:0219-4988
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Container-title:Journal of Algebra and Its Applications
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language:en
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Short-container-title:J. Algebra Appl.
Author:
Khudoyberdiyev A. Kh.1ORCID,
Sheraliyeva S. A.1
Affiliation:
1. Institute of Mathematics Academy of Sciences of Uzbekistan, National University of Uzbekistan, Tashkent 100174, Uzbekistan
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].
Funder
Ministry of Higher Education, Science and Innovations of the Republic of Uzbekistan
Publisher
World Scientific Pub Co Pte Ltd
Subject
Applied Mathematics,Algebra and Number Theory