Automorphism of a root system
= Automorphism of a root system
An automorphism of a <root system> $\Phi\subset E$ is an <orthogonal transformation> of $E$ mapping $\Phi$ onto itself. The <Weyl group> is a subgroup of this automorphism group; additional automorphisms can act nontrivially on a <Dynkin diagram> while preserving a <root basis>.