Volume 9, Issue 1 (5-2023)                   mmr 2023, 9(1): 164-188 | Back to browse issues page

XML Persian Abstract Print


Download citation:
BibTeX | RIS | EndNote | Medlars | ProCite | Reference Manager | RefWorks
Send citation to:

Golestani N. Categorical Relation between Dimension Groups, C*-algebras, and Cantor Minimal Systems. mmr 2023; 9 (1) :164-188
URL: http://mmr.khu.ac.ir/article-1-3196-en.html
Tarbiat Modares University , n.golestani@modares.ac.ir
Abstract:   (785 Views)
In this paper, we construct a direct limit functor from the category of Bratteli diagrams to the category of dimension groups and we prove that it is an equivalence of categories. The notion of a classification functor was introduced by Elliott in 2010 for classification of separable C*-algebras, which is a functor from a (complicated) category to another (concrete) functor reducing the verification of isomorphism of two objects in the first category to verification of isomorphism of their images in the second category. Using this notion, we obtain several classification functors between the categories of dimension groups, C*-algebras, and Cantor minimal systems, leading to functorial formulations and generalizations of results of Giordano, Putnam, and Skau.
Full-Text [PDF 1353 kb]   (215 Downloads)    
Type of Study: S | Subject: Operator theorey
Received: 2021/05/8 | Revised: 2024/01/7 | Accepted: 2021/07/11 | Published: 2023/06/20 | ePublished: 2023/06/20

Add your comments about this article : Your username or Email:
CAPTCHA

Send email to the article author


Rights and permissions
Creative Commons License This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

© 2024 CC BY-NC 4.0 | Mathematical Researches

Designed & Developed by : Yektaweb