We prove that every automorphism of the category of free Lie algebras is a semi-inner automorphism. This solves Problem 3.9 from [G. Mashevitzky, B. Plotkin, E. Plotkin, Electron. Res. Announc. Amer. Math. Soc. 8 (2002) 1-10] for Lie algebras.
Bibliographical noteFunding Information:
* Corresponding author. E-mail address: email@example.com (G. Mashevitzky). 1 This work is partially supported by the Emmy Noether Institute for Mathematics and the Minerva Foundation of Germany, by the Excellency Center of the Israel Science Foundation “Group Theoretic Methods in the Study of Algebraic Varieties” and by INTAS 00-566.