| Description |
1 online resource (vii, 97 pages) : illustrations |
| Series |
Memoirs of the American Mathematical Society, 0065-9266 ; volume 257, number 1233 |
|
Memoirs of the American Mathematical Society ; no. 1233. 0065-9266
|
| Contents |
Cover; Title page; Introduction; From classification to nuclear dimension; Outline of the proof of Theorem D; Structure of the paper; Acknowledgements; Chapter 1. Preliminaries; 1.1. Order zero maps; 1.2. Traces and Cuntz comparison; 1.3. Ultraproducts and the reindexing argument; Chapter 2. A 2 x 2 matrix trick; Chapter 3. Ultrapowers of trivial *-bundles; 3.1. Continuous *-bundles; 3.2. Tensor products, ultraproducts and McDuff bundles; 3.3. Strict comparison of relative commutant sequence algebras for McDuff bundles; 3.4. Traces on a relative commutant |
|
3.5. Unitary equivalence of maps into ultraproductsChapter 4. Property (SI) and its consequences; 4.1. Property (SI); 4.2. Proof of Theorem 4.1; Chapter 5. Unitary equivalence of totally full positive elements; 5.1. Proof of Theorem 5.1; 5.2. Theorem D; Chapter 6. 2-coloured equivalence; Chapter 7. Nuclear dimension and decomposition rank; Chapter 8. Quasidiagonal traces; Chapter 9. Kirchberg algebras; Addendum; Bibliography; Back Cover |
| Summary |
The authors introduce the concept of finitely coloured equivalence for unital ̂*-homomorphisms between \mathrm Ĉ*-algebras, for which unitary equivalence is the 1-coloured case. They use this notion to classify ̂*-homomorphisms from separable, unital, nuclear \mathrm Ĉ*-algebras into ultrapowers of simple, unital, nuclear, \mathcal Z-stable \mathrm Ĉ*-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 [they] calculate the nuclear dimension of non-AF, simple, sep-arable, 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, [they] derive a "homotopy equivalence implies isomorphism" result for large classes of C∗-algebras with finite nuclear dimension |
| Bibliography |
Includes bibliographical references (pages 93-97) |
| Notes |
"January 2019, Volume 257, Number 1233 (third of 6 numbers)." |
|
Print version record |
| Subject |
C*-algebras.
|
|
Homomorphisms (Mathematics)
|
|
Extremal problems (Mathematics)
|
|
MATHEMATICS -- Algebra -- Intermediate.
|
|
Álgebra
|
|
C*-algebras
|
|
Extremal problems (Mathematics)
|
|
Homomorphisms (Mathematics)
|
| Form |
Electronic book
|
| Author |
Bosa, Joan, 1985- author.
|
| ISBN |
1470449498 |
|
9781470449490 |
|
