On the Nullity of Lie Algebras zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONM Helena Albuquerque* zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIH Depatiamento de M atemcitica Faculdade de Cihcias Universidade de Coimbra 3000 Coimbra, Portugal and Albert0 Elduque+ Departamento de M atemciticas Universidud de Zaragoza 50009 Zaragoza, Spain zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJ Submitted by Richard A. BruaIdi ABSTRACT This paper deals with the problem of the determination of the nullity of a finite dimensional Lie algebra L over a field of characteristic 0. If L is solvable, we get this nullity. In general, we obtain a natural number m such that m Q nul(L) < m + 2. 1. INTRODUCTION A subset X of a Lie algebra L is said to generate L if L is the smallest linear subspace closed under the Lie product and containing X. The nullity of L is defined to be the minimum number of elements which generate L; we shall denote it by nul(L). Throughout this paper we shall study the problem of the determination of the nullity of any finite dimensional Lie algebra over a field of char- acteristic 0. *Supported by Centro de Matematica da Universidade de Coimbra-INIC and by Project0 no. 87/62-JNICT. tPartiaIly supported by the DGICYT (PS 87-0054). LINEAR ALGEBRA zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA AND ITS APPLICATIONS 166:195-206 (1992) 0 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA Elsevier Science Publishing Co., Inc., 1992 195 655 Avenue of the Americas, New York, NY 10010 0024-3795/92/$5.00