The nuclear dimension of O8-stable C*-algebras

被引：14

作者：

Bosa, Joan ^{[1
]}

Gabe, James ^{[2
]}

Sims, Aidan ^{[3
]}

White, Stuart ^{[4
]}

机构：

[1] Univ Zaragoza, Dept Matemat, C Pedro Cerbuna 12, Zaragoza 50009, Spain

[2] Univ Southern Denmark, Dept Math & Comp Sci, Odense, Denmark

[3] Univ Wollongong, Sch Math & Appl Stat, Wollongong, NSW 2522, Australia

[4] Univ Oxford, Math Inst, Radcliffe Observ Quarter, Woodstock Rd, Oxford OX2 6GG, England

来源：

ADVANCES IN MATHEMATICS | 2022年 / 401卷

基金：

澳大利亚研究理事会; 英国工程与自然科学研究理事会;

关键词：

C*-algebra; Nuclear dimension; REAL RANK; COVERING DIMENSION; DECOMPOSITION RANK; CLASSIFICATION; ZERO; INVARIANT; PROPERTY;

D O I：

10.1016/j.aim.2022.108250

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that every nuclear O-infinity-stable *-homomorphism with a separable exact domain has nuclear dimension at most 1. In particular separable, nuclear, O-infinity-stable C* algebras have nuclear dimension 1. We also characterise when O-infinity-stable C*-algebras have finite decomposition rank in terms of quasidiagonality and primitive-ideal structure, and determine when full O-2-stable *-homomorphisms have nuclear dimension 0. (c) 2022 Elsevier Inc. All rights reserved.

引用

页数：51

共 62 条

[1]

[Anonymous], 1979, L.M.S. Monographs

[2] Classification of real rank zero, purely infinite C*-algebras with at most four primitive ideals [J].

Arklint, Sara E. ;

Restorff, Gunnar ;

Ruiz, Efren .

JOURNAL OF FUNCTIONAL ANALYSIS, 2016, 271 (07) :1921-1947

[3] The Rokhlin property vs. Rokhlin dimension 1 on unital Kirchberg algebras [J].

Barlak, Selcuk ;

Enders, Dominic ;

Matui, Hiroki ;

Szabo, Gabor ;

Winter, Wilhelm .

JOURNAL OF NONCOMMUTATIVE GEOMETRY, 2015, 9 (04) :1383-1393

[4]

Blackadar B., 2006, Operator Algebras. Theory of C*-Algebras and Von Neumann Algebras

[5] THE STRUCTURE OF STABLE ALGEBRAICALLY SIMPLE C-STAR-ALGEBRAS [J].

BLACKADAR, BE ;

CUNTZ, J .

AMERICAN JOURNAL OF MATHEMATICS, 1982, 104 (04) :813-822

[6] Covering Dimension of C*-Algebras and 2-Coloured Classification [J].

Bosa, Joan ;

Brown, Nathanial P. ;

Sato, Yasuhiko ;

Tikuisis, Aaron ;

White, Stuart ;

Winter, Wilhelm .

MEMOIRS OF THE AMERICAN MATHEMATICAL SOCIETY, 2019, 257 (1233) :1-+

[7]

Brown N., 2008, Graduate Studies in Mathematics, V88

[8]

Brown NP, 2006, MEM AM MATH SOC, V184, P1

[9]

Carlsen T., 2017, T AM MATH SOC B, V4, P1

[10]

Castillejos J, 2021, INVENT MATH, V224, P245, DOI 10.1007/s00222-020-01013-1

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