RT - Journal Article
T1 - Categorical Relation between Dimension Groups, C*-algebras, and Cantor Minimal Systems
JF - khu-mmr
YR - 2023
JO - khu-mmr
VO - 9
IS - 1
UR - http://mmr.khu.ac.ir/article-1-3196-en.html
SP - 164
EP - 188
K1 - classification functor
K1 - dimension group
K1 - Bratteli diagram
K1 - C*-algebra
K1 - Cantor minimal system
K1 - orbit equivalence
AB - 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.
LA eng
UL http://mmr.khu.ac.ir/article-1-3196-en.html
M3
ER -