Automorphisms on complex simple Lie algebras of order 3

Abstract EN

For complex simple Lie algebras, the article provides the classification of all automorphisms of order 3.

The method is an extension of Dynkin diagrams so that the classification is a listing of diagrams that represent automorphisms of order 3.

This work extends an earlier result on automorphisms of order 2.

As an application, it shows that for automorphisms of orders 2 and 3 only, the invariant subalgebra determines the automorphism.