C*-algebras of right LCM one-relator monoids and Artin-Tits monoids of finite type

Abstract

WestudyC*-algebrasgeneratedbyleftregularrepresentationsofrightLCM one-relator monoids and Artin–Tits monoids of finite type. We obtain structural results concerning nuclearity, ideal structure and pure infiniteness. Moreover, we compute K- theory. Based on our K-theory results, we develop a new way of computing K-theory for certain group C*-algebras and crossed products.