The Cuntz semigroup of unital commutative AI-algebras

被引：2
作者：
Vilalta, Eduard [1 ]
机构：
[1] Univ Autonoma Barcelona, Dept Matematiques, Bellaterra, Spain
来源：
CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES | 2023年 / 75卷 / 06期
关键词：
C-*-algebras; Cuntz semigroups; AI-algebras; CLASSIFICATION;
D O I：
10.4153/S0008414X22000542
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We provide an abstract characterization for the Cuntz semigroup of unital commutative AI-algebras, as well as a characterization for abstract Cuntz semigroups of the form Lsc (overline N) for some T-1-space X. In our investigations, we also uncover new properties that the Cuntz semigroup of all AI-algebras satisfies.
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页码：1831 / 1868
页数：38
相关论文
共 25 条
  • [1] C*-ALGEBRAS OF STABLE RANK ONE AND THEIR CUNTZ SEMIGROUPS
    Antoine, Ramon
    Perera, Francesc
    Robert, Leonel
    Thiel, Hannes
    [J]. DUKE MATHEMATICAL JOURNAL, 2022, 171 (01) : 33 - 99
  • [2] Abstract Bivariant Cuntz Semigroups
    Antoine, Ramon
    Perera, Francesc
    Thiel, Hannes
    [J]. INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2020, 2020 (17) : 5342 - 5386
  • [3] Tensor Products and Regularity Properties of Cuntz Semigroups
    Antoine, Ramon
    Perera, Francesc
    Thiel, Hannes
    [J]. MEMOIRS OF THE AMERICAN MATHEMATICAL SOCIETY, 2018, 251 (1199) : 1 - +
  • [4] Pullbacks, C(X)-algebras, and their Cuntz semigroup
    Antoine, Ramon
    Perera, Francesc
    Santiago, Luis
    [J]. JOURNAL OF FUNCTIONAL ANALYSIS, 2011, 260 (10) : 2844 - 2880
  • [5] Ara P, 2011, CONTEMP MATH, V534, P1
  • [6] Uniformly based Cuntz semigroups and approximate intertwinings
    Cantier, Laurent
    [J]. INTERNATIONAL JOURNAL OF MATHEMATICS, 2022, 33 (09)
  • [7] On Inductive Limits of Type-I C*-Algebras with One-Dimensional Spectrum
    Ciuperca, Alin
    Elliott, George A.
    Santiago, Luis
    [J]. INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2011, 2011 (11) : 2577 - 2615
  • [8] A Remark on Invariants for C*-Algebras of Stable Rank One
    Ciuperca, Alin
    Elliott, George A.
    [J]. INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2008, 2008
  • [9] The Cuntz semigroup as an invariant for C*-algebras
    Coward, Kristofer T.
    Elliott, George A.
    Ivanescu, Cristian
    [J]. JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 2008, 623 : 161 - 193
  • [10] DIMENSION FUNCTIONS ON SIMPLE C-STAR-ALGEBRAS
    CUNTZ, J
    [J]. MATHEMATISCHE ANNALEN, 1978, 233 (02) : 145 - 153
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