ACTA MATHEMATICA
UNIVERSITATIS COMENIANAE




Vol. LXXVII, 1 (2008)
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






Acta Mathematica Universitatis Comenianae
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