Covering dimension of C*-algebras and 2-coloured classification
| Autor: | Bosa, Joan, Brown, Nathanial P., Sato, Yasuhiko, Tikuisis, Aaron, White, Stuart, Winter, Wilhelm |
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| Rok vydání: | 2015 |
| Předmět: | |
| Zdroj: | Mem. Amer. Math. Soc. 257(1233), 2019 |
| Druh dokumentu: | Working Paper |
| Popis: | We introduce the concept of finitely coloured equivalence for unital *-homomorphisms between C*-algebras, for which unitary equivalence is the 1-coloured case. We use this notion to classify *-homomorphisms from separable, unital, nuclear C*-algebras into ultrapowers of simple, unital, nuclear, Z-stable 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 we calculate the nuclear dimension of non-AF, simple, separable, unital, nuclear, Z-stable 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, we derive a "homotopy equivalence implies isomorphism" result for large classes of C*-algebras with finite nuclear dimension. Comment: 93 Pages. Final accepted version. Mem. Amer. Math. Soc., to appear |
| Databáze: | arXiv |
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