A Steinberg algebra approach to \'etale groupoid C*-algebras

Autor:	Clark, Lisa Orloff, Zimmerman, Joel
Rok vydání:	2022
Předmět:	Mathematics - Operator Algebras Mathematics - Rings and Algebras
Druh dokumentu:	Working Paper
Popis:	We construct the full and reduced C*-algebras of an ample groupoid from its complex Steinberg algebra. We also show that our construction gives the same C*-algebras as the standard constructions. In the last section, we consider an arbitrary locally compact, second-countable, \'etale groupoid, possibly non-Hausdorff. Using the techniques developed for Steinberg algebras, we show that every $*$-homomorphism from Connes' space of functions to $B(\mathcal{H})$ is automatically I-norm bounded. Previously, this was only known for Hausdorff groupoids. Comment: 20 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2203.00179 Zobrazit plný text záznamu View this record from Arxiv