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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 |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Providence, RI :
American Mathematical Society,
2019.
|
| Colección: | Memoirs of the American Mathematical Society ;
no. 1233. |
| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 003 | OCoLC | ||
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| 020 | |a 1470449498 | ||
| 020 | |a 9781470449490 |q (electronic bk.) | ||
| 020 | |z 9781470434700 |q (alk. paper) | ||
| 020 | |z 1470434709 |q (alk. paper) | ||
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| 035 | |a (OCoLC)1084978657 | ||
| 050 | 4 | |a QC20.7.C14 |b C68 2019 | |
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| 245 | 0 | 0 | |a Covering dimension of C*-algebras and 2-coloured classification / |c Joan Bosa [and five others]. |
| 264 | 1 | |a Providence, RI : |b American Mathematical Society, |c 2019. | |
| 264 | 4 | |c ©2019 | |
| 300 | |a 1 online resource (vii, 97 pages) : |b illustrations | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 1 | |a Memoirs of the American Mathematical Society, |x 0065-9266 ; |v volume 257, number 1233 | |
| 504 | |a Includes bibliographical references (pages 93-97) | ||
| 588 | 0 | |a Print version record. | |
| 500 | |a "January 2019, Volume 257, Number 1233 (third of 6 numbers)." | ||
| 505 | 0 | |a 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 | |
| 505 | 8 | |a 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 | |
| 520 | |a 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. | ||
| 590 | |a ProQuest Ebook Central |b Ebook Central Academic Complete | ||
| 650 | 0 | |a C*-algebras. | |
| 650 | 0 | |a Homomorphisms (Mathematics) | |
| 650 | 0 | |a Extremal problems (Mathematics) | |
| 650 | 6 | |a C*-algèbres. | |
| 650 | 6 | |a Homomorphismes (Mathématiques) | |
| 650 | 6 | |a Problèmes extrémaux (Mathématiques) | |
| 650 | 7 | |a MATHEMATICS |x Algebra |x Intermediate. |2 bisacsh | |
| 650 | 7 | |a Álgebra |2 embne | |
| 650 | 7 | |a C*-algebras |2 fast | |
| 650 | 7 | |a Extremal problems (Mathematics) |2 fast | |
| 650 | 7 | |a Homomorphisms (Mathematics) |2 fast | |
| 700 | 1 | |a Bosa, Joan, |d 1985- |e author. |1 https://id.oclc.org/worldcat/entity/E39PCjthqjQV97fCWVVJdq6XFq | |
| 758 | |i has work: |a Covering dimension of C*-algebras and 2-coloured classification (Text) |1 https://id.oclc.org/worldcat/entity/E39PCGYDfX4RCcyGYrf69Q3Xq3 |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
| 776 | 0 | 8 | |i Print version: |t Covering dimension of C*-algebras and 2-coloured classification. |d [Providence, Rhode Island] : American Mathematical Society, 2019 |z 9781470434700 |w (DLC) 2018053302 |w (OCoLC)1074297179 |
| 830 | 0 | |a Memoirs of the American Mathematical Society ; |v no. 1233. |x 0065-9266 | |
| 856 | 4 | 0 | |u https://ebookcentral.uam.elogim.com/lib/uam-ebooks/detail.action?docID=5725359 |z Texto completo |
| 938 | |a Askews and Holts Library Services |b ASKH |n AH37445227 | ||
| 938 | |a ProQuest Ebook Central |b EBLB |n EBL5725359 | ||
| 938 | |a EBSCOhost |b EBSC |n 2042357 | ||
| 938 | |a YBP Library Services |b YANK |n 16094608 | ||
| 994 | |a 92 |b IZTAP | ||