Higher-rank graph C*-algebras:: An inverse semigroup and groupoid approach

被引：61
|
作者：
Farthing, C
Muhly, PS
Yeend, T
机构：
[1] Univ Iowa, Dept Math, Iowa City, IA 52242 USA
[2] Univ Newcastle, Dept Math, Newcastle, NSW 2308, Australia
来源：
SEMIGROUP FORUM | 2005年 / 71卷 / 02期
基金：
美国国家科学基金会;
关键词：
graph algebra; Cuntz-Krieger algebra; higher-rank graph; groupoid; inverse semigroup;
D O I：
10.1007/s00233-005-0512-2
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We provide inverse semigroup and groupoid models for the Toeplitz and Cuntz-Krieger algebras of finitely aligned higher-rank graphs. Using these models, we prove a uniqueness theorem for the Cuntz-Krieger algebra.
引用
收藏
页码：159 / 187
页数：29
相关论文
共 50 条
  • [1] Higher-Rank Graph C *-Algebras: An Inverse Semigroup and Groupoid Approach
    Cynthia Farthing
    Paul S. Muhly
    Trent Yeend
    [J]. Semigroup Forum, 2005, 71 : 159 - 187
  • [2] Groupoid models for the C*-algebras of topological higher-rank graphs
    Yeend, Trent
    [J]. JOURNAL OF OPERATOR THEORY, 2007, 57 (01) : 95 - 120
  • [3] ON TWISTED HIGHER-RANK GRAPH C*-ALGEBRAS
    Kumjian, Alex
    Pask, David
    Sims, Aidan
    [J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2015, 367 (07) : 5177 - 5216
  • [4] BRANCHING SYSTEMS FOR HIGHER-RANK GRAPH C*-ALGEBRAS
    Goncalves, Daniel
    Li, Hui
    Royer, Danilo
    [J]. GLASGOW MATHEMATICAL JOURNAL, 2018, 60 (03) : 731 - 751
  • [5] Entropy of shifts on higher-rank graph C*-algebras
    Skalski, Adam
    Zacharias, Joachim
    [J]. HOUSTON JOURNAL OF MATHEMATICS, 2008, 34 (01): : 269 - 282
  • [6] SPECTRAL TRIPLES FOR HIGHER-RANK GRAPH C*-ALGEBRAS
    Farsi, Carla
    Gillaspy, Elizabeth
    Julien, Antoine
    Kang, Sooran
    Packer, Judith
    [J]. MATHEMATICA SCANDINAVICA, 2020, 126 (02) : 321 - 338
  • [7] A groupoid approach to discrete inverse semigroup algebras
    Steinberg, Benjamin
    [J]. ADVANCES IN MATHEMATICS, 2010, 223 (02) : 689 - 727
  • [8] UNIQUENESS THEOREMS FOR TOPOLOGICAL HIGHER-RANK GRAPH C*-ALGEBRAS
    Renault, Jean
    Sims, Aidan
    Williams, Dana P.
    Yeend, Trent
    [J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2018, 146 (02) : 669 - 684
  • [9] Purely Atomic Representations of Higher-Rank Graph C*-Algebras
    Farsi, Carla
    Gillaspy, Elizabeth
    Jorgensen, Palle
    Kang, Sooran
    Packer, Judith
    [J]. INTEGRAL EQUATIONS AND OPERATOR THEORY, 2018, 90 (06)
  • [10] Groupoid and inverse semigroup presentations of ultragraph C*-algebras
    Alberto E. Marrero
    Paul S. Muhly
    [J]. Semigroup Forum, 2008, 77 : 399 - 422
12345