Periodic automorphisms of the free Lie algebra of rank 3 (Q642061)

The author proves the following result. Theorem. Each automorphism of finite order of the free Lie algebra of rank 3 over an algebraically closed field is conjugate to a linear automorphism provided that the field characteristic does not divide the automorphism order. The proof essentially relies on the fact that the automorphism group of a finitely generated free algebra of a Schreier variety is finitely presented \textit{U. U. Umirbaev} [J. Algebra 314, No. 1, 209--225 (2007; Zbl 1132.17002)].