Rank one Lie algebras (Q1057355)

The main theorem of the paper under review has been announced [Contemp. Math. 13, 263-265 (1982; Zbl 0504.17003)]: Let L be a finite-dimensional simple Lie algebra over an algebraically closed field of prime characteristic \(p>7\). If L has a one-dimensional Cartan subalgebra, then L is isomorphic to the three-dimensional algebra \({\mathfrak sl}(2)\) or to an Albert-Zassenhaus Lie algebra. As the authors mention, the result is true for characteristics 5 and 7 as well. The proof including the cases \(p=5\) and \(p=7\) is based on more technical calculations and is not given in the paper.