Solvable extensions of a special class of nilpotent Lie algebras

Shabanskaya, A.; Thompson, Gerard

doi:10.5817/am2013-3-141

Cited by 6 publications

(2 citation statements)

References 15 publications

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“…By using the same method, the results for the case of dimension 6 were also achieved by Mubarakzyanov [21] and Turkowski [40]. Furthermore, results in [23,27,[29][30][31][32][33][34][35]41] show that this method seems to be very effective.…”

Section: Introductionmentioning

confidence: 57%

Classification of 7-dimensional solvable Lie algebras having 5-dimensional nilradicals

Le¹,

Nguyen²,

Nguyen³

et al. 2021

Preprint

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This paper presents a classification of 7-dimensional real and complex indecomposable solvable Lie algebras having some 5-dimensional nilradicals. Afterwards, we combine our results with those of Rubin and Winternitz (1993), Ndogmo and Winternitz (1994), Šnobl and Winternitz (2005, 2009), Šnobl and Karásek (2010) to obtain a complete classification of 7-dimensional real and complex indecomposable solvable Lie algebras with 5-dimensional nilradicals. In association with Gong (1998), Parry (2007), Hindeleh andThompson (2008), we achieve a classification of 7-dimensional real and complex indecomposable solvable Lie algebras.

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Section: Introductionmentioning

confidence: 57%

Classification of 7-dimensional solvable Lie algebras having 5-dimensional nilradicals

Le¹,

Nguyen²,

Nguyen³

et al. 2021

Preprint

View full text Add to dashboard Cite

show abstract

“…By using these relationships the classification of solvable extensions has been given for the following classes of nilpotent Lie algebras in low-dimensions with Abelian [29,30], Heisenberg [33], Borel [41], N-graded [9], filiform and quasifiliform nilradicals [39,40] (also see [38] and references therein). A few nilradicals cases are given in [34,35,36]. In the finite-dimensional case, the concept of filiform Lie algebra has been introduced by Vergne in [43].…”

Section: Introductionmentioning

confidence: 99%