Characterising large‐type Artin groups

Abstract We show that the class of large‐type Artin groups is invariant under isomorphism, in stark contrast with the corresponding situation for Coxeter groups. We obtain this result by providing a purely algebraic characterisation of large‐type Artin groups (i.e. independent of the presentation graph). As a corollary, we completely describe the Artin groups isomorphic to a given large‐type Artin group, and characterise those large‐type Artin groups that are rigid.