On the nullity of Lie algebras (Q1185059)

Let \(L\) be a finite-dimensional Lie algebra over a field of characteristic 0. The nullity of \(L\), \(\text{nul} (L)\), is the minimum number of elements which generate \(L\). Let \(L\) be a solvable Lie algebra written as a direct sum of its abelian ideals \(V_ i\) and an abelian subalgebra \(C\). The authors obtain the value of \(\text{nul} (L)\) in terms of the dimensions of \(C\) and the \(V_ i\)'s. For a nonsolvable Lie algebra \(L\), they obtain a natural number \(m\) such that \(m\leq \text{nul} (L)\leq m+2\).