Covering Dimension of C*-Algebras and 2-Coloured Classification. (Record no. 9063)
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| 000 -LEADER | |
|---|---|
| fixed length control field | 04123nam a22004933i 4500 |
| 001 - CONTROL NUMBER | |
| control field | EBC5725359 |
| 003 - CONTROL NUMBER IDENTIFIER | |
| control field | MiAaPQ |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20240724113622.0 |
| 006 - FIXED-LENGTH DATA ELEMENTS--ADDITIONAL MATERIAL CHARACTERISTICS | |
| fixed length control field | m o d | |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION | |
| fixed length control field | cr cnu|||||||| |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 240724s2018 xx o ||||0 eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9781470449490 |
| Qualifying information | (electronic bk.) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| Canceled/invalid ISBN | 9781470434700 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (MiAaPQ)EBC5725359 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (Au-PeEL)EBL5725359 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (OCoLC)1084978657 |
| 040 ## - CATALOGING SOURCE | |
| Original cataloging agency | MiAaPQ |
| Language of cataloging | eng |
| Description conventions | rda |
| -- | pn |
| Transcribing agency | MiAaPQ |
| Modifying agency | MiAaPQ |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER | |
| Classification number | QC20.7.C14 .B673 2019 |
| 082 0# - DEWEY DECIMAL CLASSIFICATION NUMBER | |
| Classification number | 512.556 |
| 100 1# - MAIN ENTRY--PERSONAL NAME | |
| Personal name | Bosa, Joan. |
| 245 10 - TITLE STATEMENT | |
| Title | Covering Dimension of C*-Algebras and 2-Coloured Classification. |
| 250 ## - EDITION STATEMENT | |
| Edition statement | 1st ed. |
| 264 #1 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE | |
| Place of production, publication, distribution, manufacture | Providence : |
| Name of producer, publisher, distributor, manufacturer | American Mathematical Society, |
| Date of production, publication, distribution, manufacture, or copyright notice | 2018. |
| 264 #4 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE | |
| Date of production, publication, distribution, manufacture, or copyright notice | ©2019. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | 1 online resource (112 pages) |
| 336 ## - CONTENT TYPE | |
| Content type term | text |
| Content type code | txt |
| Source | rdacontent |
| 337 ## - MEDIA TYPE | |
| Media type term | computer |
| Media type code | c |
| Source | rdamedia |
| 338 ## - CARRIER TYPE | |
| Carrier type term | online resource |
| Carrier type code | cr |
| Source | rdacarrier |
| 490 1# - SERIES STATEMENT | |
| Series statement | Memoirs of the American Mathematical Society Series ; |
| Volume/sequential designation | v.257 |
| 505 0# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | 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 ultraproducts -- Chapter 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 ## - SUMMARY, ETC. | |
| Summary, etc. | 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. |
| 588 ## - SOURCE OF DESCRIPTION NOTE | |
| Source of description note | Description based on publisher supplied metadata and other sources. |
| 590 ## - LOCAL NOTE (RLIN) | |
| Local note | Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | C*-algebras. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Homomorphisms (Mathematics). |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Extremal problems (Mathematics). |
| 655 #4 - INDEX TERM--GENRE/FORM | |
| Genre/form data or focus term | Electronic books. |
| 700 1# - ADDED ENTRY--PERSONAL NAME | |
| Personal name | Brown, Nathanial P. |
| 700 1# - ADDED ENTRY--PERSONAL NAME | |
| Personal name | Sato, Yasuhiko. |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
| Relationship information | Print version: |
| Main entry heading | Bosa, Joan |
| Title | Covering Dimension of C*-Algebras and 2-Coloured Classification |
| Place, publisher, and date of publication | Providence : American Mathematical Society,c2018 |
| International Standard Book Number | 9781470434700 |
| 797 2# - LOCAL ADDED ENTRY--CORPORATE NAME (RLIN) | |
| Corporate name or jurisdiction name as entry element | ProQuest (Firm) |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE | |
| Uniform title | Memoirs of the American Mathematical Society Series |
| 856 40 - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | <a href="https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=5725359">https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=5725359</a> |
| Public note | Click to View |
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