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Covering dimension of C*-algebras and 2-coloured classification /
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 o...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Providence, RI :
American Mathematical Society,
2019.
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| Colección: | Memoirs of the American Mathematical Society ;
no. 1233. |
| Temas: | |
| Acceso en línea: | Texto completo |
| Sumario: | 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 [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. |
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| Notas: | "January 2019, Volume 257, Number 1233 (third of 6 numbers)." |
| Descripción Física: | 1 online resource (vii, 97 pages) : illustrations |
| Bibliografía: | Includes bibliographical references (pages 93-97) |
| ISBN: | 1470449498 9781470449490 |
| ISSN: | 0065-9266 ; |