Geodesic
Left regular representations of Garside categories I. C*-algebras and groupoids
Glasgow mathematical journal, Tome 65 (2023), pp. S53-S86

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DOI

We initiate the study of C*-algebras and groupoids arising from left regular representations of Garside categories, a notion which originated from the study of Braid groups. Every higher rank graph is a Garside category in a natural way. We develop a general classification result for closed invariant subspaces of our groupoids as well as criteria for topological freeness and local contractiveness, properties which are relevant for the structure of the corresponding C*-algebras. Our results provide a conceptual explanation for previous results on gauge-invariant ideals of higher rank graph C*-algebras. As another application, we give a complete analysis of the ideal structures of C*-algebras generated by left regular representations of Artin–Tits monoids. 
Li, Xin. Left regular representations of Garside categories I. C*-algebras and groupoids. Glasgow mathematical journal, Tome 65 (2023), pp. S53-S86. doi: 10.1017/S0017089522000106
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     author = {Li, Xin},
     title = {Left regular representations of {Garside} categories {I.} {C*-algebras} and groupoids},
     journal = {Glasgow mathematical journal},
     pages = {S53--S86},
     year = {2023},
     volume = {65},
     number = {S1},
     doi = {10.1017/S0017089522000106},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089522000106/}
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