On the component group of the automorphism group of a Lie group

Abstract

AbstractLet G be a Lie group, Go the connected component of G that contains the identity, and Aut G the group of all topological automorphisms of G. In the case when G/Go is finite and G has a faithful representation, we obtain a necessary and sufficient condition for G so that Aut G has finitely many components in terms of the maximal central torus in Go.