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Solvable quadratic Lie algebras in low dimensions

2012/04/21 by Tien Dat Pham, Pham, Tien Dat, Anh Vu Le +4
Mathematics · Physics and Astronomy · #17B05 #17B30 #17B40 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Rings and Algebras (math.RA) #math.RA #msc:17B05 #msc:17B30 #msc:17B40

paper · pdf · doi:10.48550/arxiv.1204.4787

10 pages

arxiv created 2012/04/21 · openalex publication_date 2012/04/21 · arxiv updated 2012/04/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we classify solvable quadratic Lie algebras up to dimension 6. In dimensions smaller than 6, we use the Witt decomposition given in \citeBou59 and a result in \citePU07 to obtain two non-Abelian indecomposable solvable quadratic Lie algebras. In the case of dimension 6, by applying the method of double extension given in \citeKac85 and \citeMR85 and the classification result of singular quadratic Lie algebras in \citeDPU, we have three families of solvable quadratic Lie algebras which are indecomposable and not isomorphic.

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