On quasi-filiform Lie algebras admitting a torus of derivations. (Sur les algèbres de Lie quasi-filiformes admettant un tore de dérivations.) (English) Zbl 1172.17006

García Vergnolle, L.

Manuscr. Math. 124, No. 4, 489-505 (2007).

The main theorem of the paper under review provides a classification for the quasi-filiform Lie algebras that allow for nontrivial diagonalizable derivations. We recall that a nilpotent Lie algebra of dimension \(n\) is said to be quasi-filiform if its nilpotency index is equal to \(n-2\). The present classification is based on the classification of the naturally graded quasi-filiform algebras given by J. R. Gómez and A. Jiménez-Merchán [J. Algebra 256, No. 1, 211–228 (2002; Zbl 1030.17007)].

Reviewer: Daniel Beltiţă (Bucureşti)

MSC:

17B30	Solvable, nilpotent (super)algebras
17B70	Graded Lie (super)algebras

Keywords:

nilpotent Lie algebra; filiform Lie algebra; torus of derivations

Citations:

Zbl 1030.17007

References:

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