Can solvable extensions of a nilpotent subalgebra be useful in the classification of solvable algebras with the given nilradical?

Abstract

We construct all solvable Lie algebras with a specific n-dimensional nilradical n_{n,3} which contains the previously studied filiform nilpotent algebra n_{n-2,1} as a subalgebra but not as an ideal. Rather surprisingly it turns out that the classification of such solvable algebras can be reduced to the classification of solvable algebras with the nilradical n_{n-2,1} together with one additional case. Also the sets of invariants of coadjoint representation of n_{n,3} and its solvable extensions are deduced from this reduction. In several cases they have polynomial bases, i.e. the invariants of the respective solvable algebra can be chosen to be Casimir invariants in its enveloping algebra.

19 pages

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Cited by in corpus (6)

• On the structure of maximal solvable extensions and of Levi extensions of nilpotent algebras
• Solvable Lie algebras with Borel nilradicals
• Classification of solvable Leibniz algebras with null-filiform nilradical
• On Solvable Lie and Leibniz Superalgebras with maximal codimension of nilradical
• Foliations formed by generic coadjoint orbits of a class of 7-dimensional real solvable Lie groups
• Solvable Leibniz superalgebras whose nilradical has the characteristic sequence $(n-1,1\mid m)$ and nilindex $n+m$