Inner Finite Order Automorphisms of Type A

Abstract

Let g be a complex simple Lie algebra, and let aut(g) be the group of all automorphisms on g. The finite order members of aut(g) have been classified by Kac, up to conjugation by g-automorphisms. In other words, this classification does not distinguish two finite order g-automorphisms σ, τ if there exists u ∈ aut(g) such that σ = u−1τu. For g = sl(n,C) and σ, τ inner, we provide a finer classification up to conjugation by inner g-automorphisms, namely we do not distinguish σ, τ only if u is an inner automorphism.