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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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