The Rokhlin property vs. Rokhlin dimension 1 on unital Kirchberg algebras

被引:10
作者
Barlak, Selcuk [1 ]
Enders, Dominic [2 ]
Matui, Hiroki [3 ]
Szabo, Gabor [4 ]
Winter, Wilhelm [4 ]
机构
[1] Univ Southern Denmark, Dept Math & Comp Sci, Campusvej 55, DK-5230 Odense M, Denmark
[2] Univ Copenhagen, Dept Math Sci, DK-2100 Copenhagen, Denmark
[3] Chiba Univ, Grad Sch Sci, Inage Ku, Chiba 2638522, Japan
[4] Univ Munster, Fachbereich Math, D-48149 Munster, Germany
基金
新加坡国家研究基金会;
关键词
Kirchberg algebra; nuclear dimension; Rokhlin dimension; C-ASTERISK-ALGEBRAS; FINITE-GROUP ACTIONS; NUCLEAR DIMENSION; DECOMPOSITION RANK; ROHLIN PROPERTY;
D O I
10.4171/JNCG/226
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We investigate outer symmetries on unital Kirchberg algebras with respect to the Rokhlin property and finite Rokhlin dimension. In stark contrast to the restrictiveness of the Rokhlin property, every such action has Rokhlin dimension at most one. A consequence of these observations is a relationship between the nuclear dimension of an O-infinity-absorbing C*-algebra and its O-2-stabilization. We also give a more direct and alternative approach to this result. Several applications of this relationship are discussed to cover a fairly large class of O-infinity-absorbing C*-algebras that turn out to have finite nuclear dimension.
引用
收藏
页码:1383 / 1393
页数:11
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