Left regular representations of Garside categories I. C^*-algebras and groupoids

Abstract We initiate the study of C * -algebras and groupoids arising from left regular representations Garside categories, a notion which originated Braid groups. Every higher rank graph is category in natural way. develop general classification result for closed invariant subspaces our as well criteria topological freeness local contractiveness, properties are relevant structure corresponding -algebras. Our results provide conceptual explanation previous on gauge-invariant ideals As another application, we give complete analysis ideal structures generated by Artin–Tits monoids.