p. 141 - 145 Solvable Lie algebras and maximal Abelian dimensions
Á. F. Tenorio Received: January 1, 2007;
Revised: November 11, 2007;
Accepted: December 18, 2007
Abstract.
In this paper some results on the structure of finite-dimensional
Lie algebras are obtained by means of the concept of maximal
abelian dimension. More concretely, a sufficient condition is
given for the solvability in finite-dimensional Lie algebras by
using maximal abelian dimensions. Besides, a necessary condition
for the nilpotency is also stated for such Lie algebras. Finally,
the maximal abelian dimension is applied to characterize the
n-dimensional nilpotent Lie algebras with maximal abelian
dimension equal to their codimension.
Keywords:
solvable Lie algebra; nilpotent Lie algebra; maximal abelian dimension.
AMS Subject classification:
Primary: 17B30;
Secondary: 17B05.
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