Online Library TheLib.net » Covering Dimension of C*-Algebras and 2-Coloured Classification
cover of the book Covering Dimension of C*-Algebras and 2-Coloured Classification

Ebook: Covering Dimension of C*-Algebras and 2-Coloured Classification

00
02.03.2024
0
0
The authors introduce the concept of finitely coloured equivalence for unital $^*$-homomorphisms between $mathrm C^*$-algebras, for which unitary equivalence is the $1$-coloured case. They use this notion to classify $^*$-homomorphisms from separable, unital, nuclear $mathrm C^*$-algebras into ultrapowers of simple, unital, nuclear, $mathcal Z$-stable $mathrm C^*$-algebras with compact extremal trace space up to $2$-coloured equivalence by their behaviour on traces; this is based on a $1$-coloured classification theorem for certain order zero maps, also in terms of tracial data. As an application the authors calculate the nuclear dimension of non-AF, simple, separable, unital, nuclear, $mathcal Z$-stable $mathrm C^*$-algebras with compact extremal trace space: it is 1. In the case that the extremal trace space also has finite topological covering dimension, this confirms the remaining open implication of the Toms-Winter conjecture. Inspired by homotopy-rigidity theorems in geometry and topology, the authors derive a "homotopy equivalence implies isomorphism" result for large classes of $mathrm C^*$-algebras with finite nuclear dimension.
Download the book Covering Dimension of C*-Algebras and 2-Coloured Classification for free or read online
Read Download
Continue reading on any device:
QR code
Last viewed books
Related books
Comments (0)
reload, if the code cannot be seen