2022/02/22 by Abror Khudoyberdiyev, Khudoyberdiyev, A. Kh., S. A. Sheraliyeva +1 · 1 citation
Materials Science · Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Mesoporous Materials and Catalysis #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.2202.10718
openalex publication_date 2022/02/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 nn, 1 and Q2n. We find all one-dimensional central extensions of the algebra nn, 1 and show that any extension of Q2n is split. After that we find one-dimensional extensions of solvable Lie algebras with nilradical nn, 1. We prove that there exists a unique non-split central extension of solvable Lie algebras with nilradical nn, 1 of maximal codimension. Moreover, all one-dimensional extensions of solvable Lie algebras with nilradical nn, 1 whose codimension is equal to one are found and compared these solvable algebras with the solvable algebras with nilradicals are one-dimensional central extension of algebra nn, 1.