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. PDF Compressed Postscript Version to read ISSN 0862-9544 (Printed edition) Faculty of Mathematics, Physics and Informatics Comenius University 842 48 Bratislava, Slovak Republic Telephone: + 421-2-60295111 Fax: + 421-2-65425882 e-Mail: amuc@fmph.uniba.sk Internet: www.iam.fmph.uniba.sk/amuc © 2008, ACTA MATHEMATICA UNIVERSITATIS COMENIANAE |