All classifiable Kirchberg algebras are C*-algebras of ample groupoids

被引：1
|
作者：
Clark, Lisa Orloff [1 ]
Fletcher, James [1 ]
Huef, Astrid An [1 ]
机构：
[1] Victoria Univ Wellington, Sch Math & Stat, POB 600, Wellington 6140, New Zealand
来源：
EXPOSITIONES MATHEMATICAE | 2020年 / 38卷 / 04期
关键词：
Simple purely infinite C*-algebra; Classification of C*-algebras; Kirchberg algebra; Groupoid; CLASSIFICATION; MODELS;
D O I：
10.1016/j.exmath.2019.06.001
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this note we show that every Kirchberg algebra in the UCT class is the C*-algebra of a Hausdorff, ample, amenable and locally contracting groupoid. The non-unital case follows from Spielberg's graph-based models for Kirchberg algebras. Our contribution is the unital case and our proof builds on Spielberg's construction. (C) 2019 Elsevier GmbH. All rights reserved.
引用
收藏
页码：559 / 565
页数：7
相关论文
共 50 条
  • [1] Colored isomorphism of classifiable C* -algebras
    Elliott, George A.
    Im, Jeffrey
    CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 2024, 76 (01): : 216 - 245
  • [2] Classification of extensions of classifiable C*-algebras
    Eilers, Soren
    Restorff, Gunnar
    Ruiz, Efren
    ADVANCES IN MATHEMATICS, 2009, 222 (06) : 2153 - 2172
  • [3] Tensor products of classifiable C*-algebras
    Lin, Huaxin
    Sun, Wei
    JOURNAL OF TOPOLOGY AND ANALYSIS, 2017, 9 (03) : 485 - 504
  • [4] Continuous fields of Kirchberg C*-algebras
    Dadarlat, M
    Pasnicu, C
    JOURNAL OF FUNCTIONAL ANALYSIS, 2005, 226 (02) : 429 - 451
  • [5] Anomalous symmetries of classifiable C*-algebras
    Evington, Samuel
    Pacheco, Sergio
    STUDIA MATHEMATICA, 2023, 270 (01) : 73 - 102
  • [6] Constructing Menger Manifold C*-Diagonals in Classifiable C*-Algebras
    Li, Xin
    INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2022, 2022 (23) : 18992 - 19053
  • [7] C∗-algebras associated to directed graphs of groups, and models of Kirchberg algebras
    Wu, Victor
    JOURNAL OF FUNCTIONAL ANALYSIS, 2025, 288 (03)
  • [8] STRONG CLASSIFICATION OF EXTENSIONS OF CLASSIFIABLE C*-ALGEBRAS
    Eilers, Soren
    Restorff, Gunnar
    Ruiz, Efren
    BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY, 2022, 59 (03) : 567 - 608
  • [9] The admissible KMS bundles on classifiable C*-algebras
    Neagu, Robert
    PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 2024,
  • [10] INCLUSIONS OF C*-ALGEBRAS OF GRADED GROUPOIDS
    Armstrong, Becky
    Clark, Lisa Orloff
    An Huef, Astrid
    JOURNAL OF OPERATOR THEORY, 2023, 89 (01) : 285 - 299
12345