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>.