Jianguo, Zha, Fixed-point-free Automorphisms of Lie Algebras, Acta Mathematica Sinica, New Series Chinese Journal of Mathematics, 5(1), 1989, pp. 95-96
In this paper we have proved that the Lie algebra L over a field F of characteristic 0 which admits a fixed-point-free automorphism of finite order is solvable, and L is nilpotent if L admits a fixed- point-free automorphism of prime order. The problem seems to be open if the field Fhas prime characteristic.