scholarly journals Uniqueness theorems for topological higher-rank graph $C^*$-algebras

2017 ◽  
Vol 146 (2) ◽  
pp. 669-684 ◽  
Author(s):  
Jean Renault ◽  
Aidan Sims ◽  
Dana P. Williams ◽  
Trent Yeend
Keyword(s):  
Uniqueness Theorems ◽  
C Algebras ◽  
Higher Rank

scholarly journals HIGHER-RANK GRAPHS AND THEIR $C^*$-ALGEBRAS

2003 ◽  
Vol 46 (1) ◽  
pp. 99-115 ◽  
Author(s):  
Iain Raeburn ◽  
Aidan Sims ◽  
Trent Yeend
Keyword(s):  
Subject Classification ◽  
Uniqueness Theorems ◽  
Local Convexity ◽  
Convexity Condition ◽  
Primary 46L05 ◽  
C Algebras ◽  
Higher Rank

AbstractWe consider the higher-rank graphs introduced by Kumjian and Pask as models for higher-rank Cuntz–Krieger algebras. We describe a variant of the Cuntz–Krieger relations which applies to graphs with sources, and describe a local convexity condition which characterizes the higher-rank graphs that admit a non-trivial Cuntz–Krieger family. We then prove versions of the uniqueness theorems and classifications of ideals for the $C^*$-algebras generated by Cuntz–Krieger families.AMS 2000 Mathematics subject classification: Primary 46L05

scholarly journals Spatial realisations of KMS states on the C⁎-algebras of higher-rank graphs

2015 ◽  
Vol 427 (2) ◽  
pp. 977-1003 ◽  
Author(s):  
Astrid an Huef ◽  
Sooran Kang ◽  
Iain Raeburn
Keyword(s):  
Kms States ◽  
C Algebras ◽  
Higher Rank

scholarly journals Simplicity of C*-algebras associated to higher-rank graphs

2007 ◽  
Vol 39 (2) ◽  
pp. 337-344 ◽  
Author(s):  
David I. Robertson ◽  
Aidan Sims
Keyword(s):  
C Algebras ◽  
Higher Rank

scholarly journals The C∗-algebras of finitely aligned higher-rank graphs

2004 ◽  
Vol 213 (1) ◽  
pp. 206-240 ◽  
Author(s):  
Iain Raeburn ◽  
Aidan Sims ◽  
Trent Yeend
Keyword(s):  
C Algebras ◽  
Higher Rank

Representations of higher-rank graph C⁎-algebras associated to Λ-semibranching function systems

2018 ◽  
Vol 468 (2) ◽  
pp. 766-798 ◽  
Author(s):  
Carla Farsi ◽  
Elizabeth Gillaspy ◽  
Palle Jorgensen ◽  
Sooran Kang ◽  
Judith Packer
Keyword(s):  
C Algebras ◽  
Higher Rank

scholarly journals BRANCHING SYSTEMS FOR HIGHER-RANK GRAPH C*-ALGEBRAS

2018 ◽  
Vol 60 (3) ◽  
pp. 731-751 ◽  
Author(s):  
DANIEL GONÇALVES ◽  
HUI LI ◽  
DANILO ROYER
Keyword(s):  
Uniqueness Theorem ◽  
Hilbert Spaces ◽  
Sufficient Condition ◽  
Single Vertex ◽  
C Algebras ◽  
Higher Rank ◽  
Concrete Representations

AbstractWe define branching systems for finitely aligned higher-rank graphs. From these, we construct concrete representations of higher-rank graph C*-algebras on Hilbert spaces. We prove a generalized Cuntz–Krieger uniqueness theorem for periodic single-vertex 2-graphs. We use this result to give a sufficient condition under which representations of periodic single-vertex 2-graph C*-algebras arising from branching systems are faithful.

scholarly journals Higher-Rank Graph C *-Algebras: An Inverse Semigroup and Groupoid Approach

2005 ◽  
Vol 71 (2) ◽  
pp. 159-187 ◽  
Author(s):  
Cynthia Farthing ◽  
Paul S. Muhly ◽  
Trent Yeend
Keyword(s):  
Inverse Semigroup ◽  
C Algebras ◽  
Higher Rank

scholarly journals Structure theory and stable rank for C*-algebras of finite higher-rank graphs

2021 ◽  
pp. 1-26
Author(s):  
David Pask ◽  
Adam Sierakowski ◽  
Aidan Sims
Keyword(s):  
Stable Rank ◽  
Structure Theory ◽  
C Algebras ◽  
Higher Rank ◽  
Stably Finite ◽  
Locally Convex

Abstract We study the structure and compute the stable rank of $C^{*}$ -algebras of finite higher-rank graphs. We completely determine the stable rank of the $C^{*}$ -algebra when the $k$ -graph either contains no cycle with an entrance or is cofinal. We also determine exactly which finite, locally convex $k$ -graphs yield unital stably finite $C^{*}$ -algebras. We give several examples to illustrate our results.

Purely Atomic Representations of Higher-Rank Graph $$\varvec{C}^{\varvec{*}}$$ C ∗ -Algebras

2018 ◽  
Vol 90 (6) ◽  
Author(s):  
Carla Farsi ◽  
Elizabeth Gillaspy ◽  
Palle Jorgensen ◽  
Sooran Kang ◽  
Judith Packer
Keyword(s):  
C Algebras ◽  
Higher Rank
Sign in / Sign up

Export Citation Format

Share Document