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Bibliographic Details
Main Author: Starling, Charles
Format: Preprint
Published: 2026
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Online Access:https://arxiv.org/abs/2604.21116
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_version_ 1866917487921070080
author Starling, Charles
author_facet Starling, Charles
contents Spielberg's construction of C*-algebras from left cancellative small categories is a common generalization for most C*-algebras one would consider to come from ``combinatorial data,'' including graph and $k$-graph C*-algebras, Li's semigroup C*-algebras, Nekrashevych's self-similar action algebras, and more. We use known groupoid models of these algebras and Exel's theory of tight representations of inverse semigroups to prove uniqueness theorems for these C*-algebras. As applications, we improve on our previous uniqueness theorem for the boundary quotient C*-algebras of right LCM monoids, and we also generalize the uniqueness theorem of Brown, Nagy, and Reznikoff for row-finite higher-rank graphs to the finitely aligned case.
format Preprint
id arxiv_https___arxiv_org_abs_2604_21116
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Uniqueness theorems for combinatorial C*-algebras
Starling, Charles
Operator Algebras
Dynamical Systems
46L05, 20M18, 18B40
Spielberg's construction of C*-algebras from left cancellative small categories is a common generalization for most C*-algebras one would consider to come from ``combinatorial data,'' including graph and $k$-graph C*-algebras, Li's semigroup C*-algebras, Nekrashevych's self-similar action algebras, and more. We use known groupoid models of these algebras and Exel's theory of tight representations of inverse semigroups to prove uniqueness theorems for these C*-algebras. As applications, we improve on our previous uniqueness theorem for the boundary quotient C*-algebras of right LCM monoids, and we also generalize the uniqueness theorem of Brown, Nagy, and Reznikoff for row-finite higher-rank graphs to the finitely aligned case.
title Uniqueness theorems for combinatorial C*-algebras
topic Operator Algebras
Dynamical Systems
46L05, 20M18, 18B40
url https://arxiv.org/abs/2604.21116