On the derived length of solvable Lie algebras (Q1113990)

The authors compute the derived length of solvable Lie algebras over an algebraically closed field of characteristic \(p\) with faithful irreducible representation of dimension \(p^n\). In particular, if \(L\) is such an algebra, then \(L^{(n+1+TR(L))}=0\) when \(TR(L)=\max \{\dim T,\;T\) a torus of \(L\}\) and \(TR(L)\) is shown to be less than or equal to \(n\). If \(L\) is nilpotent, then \(L^{(n+1)}=0\). A critical role is played by certain subalgebras of the Jacobson-Witt algebra, \(W(n,1)\).