An introduction to the classification of amenable C*-algebras:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Singapore
World Scientific
©2001
|
| Schlagworte: | |
| Online-Zugang: | FAW01 FAW02 Volltext |
| Beschreibung: | Includes bibliographical references (pages 307-316) and index The theory and applications of C*-algebras are related to fields ranging from operator theory, group representations and quantum mechanics, to non-commutative geometry and dynamical systems. By Gelfand transformation, the theory of C*-algebras is also regarded as non-commutative topology. About a decade ago, George A. Elliott initiated the program of classification of C*-algebras (up to isomorphism) by their K-theoretical data. It started with the classification of AT-algebras with real rank zero. Since then great efforts have been made to classify amenable C*-algebras, a class of C*-algebras that arises most naturally. For example, a large class of simple amenable C*-algebras is discovered to be classifiable. The application of these results to dynamical systems has been established. This book introduces the recent development of the theory of the classification of amenable C*-algebras - the first such attempt. The first three chapters present the basics of the theory of C*-algebras which are particularly important to the theory of the classification of amenable C*-algebras. Chapter 4 offers the classification of the so-called AT-algebras of real rank zero. The first four chapters are self-contained, and can serve as a text for a graduate course on C*-algebras. The last two chapters contain more advanced material. In particular, they deal with the classification theorem for simple AH-algebras with real rank zero, the work of Elliott and Gong. The book contains many new proofs and some original results related to the classification of amenable C*-algebras. As well as providing an introduction to the theory of the classification of amenable C*-algebras, it is a comprehensive reference for those more familiar with the subject |
| Beschreibung: | 1 Online-Ressource (xi, 320 pages) |
| ISBN: | 1281951439 9781281951434 9789810246808 9789812799883 9810246803 9812799885 |
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| 500 | |a The theory and applications of C*-algebras are related to fields ranging from operator theory, group representations and quantum mechanics, to non-commutative geometry and dynamical systems. By Gelfand transformation, the theory of C*-algebras is also regarded as non-commutative topology. About a decade ago, George A. Elliott initiated the program of classification of C*-algebras (up to isomorphism) by their K-theoretical data. It started with the classification of AT-algebras with real rank zero. Since then great efforts have been made to classify amenable C*-algebras, a class of C*-algebras that arises most naturally. For example, a large class of simple amenable C*-algebras is discovered to be classifiable. The application of these results to dynamical systems has been established. This book introduces the recent development of the theory of the classification of amenable C*-algebras - the first such attempt. The first three chapters present the basics of the theory of C*-algebras which are particularly important to the theory of the classification of amenable C*-algebras. Chapter 4 offers the classification of the so-called AT-algebras of real rank zero. The first four chapters are self-contained, and can serve as a text for a graduate course on C*-algebras. The last two chapters contain more advanced material. In particular, they deal with the classification theorem for simple AH-algebras with real rank zero, the work of Elliott and Gong. The book contains many new proofs and some original results related to the classification of amenable C*-algebras. As well as providing an introduction to the theory of the classification of amenable C*-algebras, it is a comprehensive reference for those more familiar with the subject | ||
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Datensatz im Suchindex
| _version_ | 1804175495755988992 |
|---|---|
| any_adam_object | |
| author | Lin, Huaxin |
| author_facet | Lin, Huaxin |
| author_role | aut |
| author_sort | Lin, Huaxin |
| author_variant | h l hl |
| building | Verbundindex |
| bvnumber | BV043093059 |
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| dewey-full | 512/.55 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.55 |
| dewey-search | 512/.55 |
| dewey-sort | 3512 255 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| id | DE-604.BV043093059 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:17:12Z |
| institution | BVB |
| isbn | 1281951439 9781281951434 9789810246808 9789812799883 9810246803 9812799885 |
| language | English |
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| physical | 1 Online-Ressource (xi, 320 pages) |
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| spelling | Lin, Huaxin Verfasser aut An introduction to the classification of amenable C*-algebras Huaxin Lin Amenable C*-algebras Singapore World Scientific ©2001 1 Online-Ressource (xi, 320 pages) txt rdacontent c rdamedia cr rdacarrier Includes bibliographical references (pages 307-316) and index The theory and applications of C*-algebras are related to fields ranging from operator theory, group representations and quantum mechanics, to non-commutative geometry and dynamical systems. By Gelfand transformation, the theory of C*-algebras is also regarded as non-commutative topology. About a decade ago, George A. Elliott initiated the program of classification of C*-algebras (up to isomorphism) by their K-theoretical data. It started with the classification of AT-algebras with real rank zero. Since then great efforts have been made to classify amenable C*-algebras, a class of C*-algebras that arises most naturally. For example, a large class of simple amenable C*-algebras is discovered to be classifiable. The application of these results to dynamical systems has been established. This book introduces the recent development of the theory of the classification of amenable C*-algebras - the first such attempt. The first three chapters present the basics of the theory of C*-algebras which are particularly important to the theory of the classification of amenable C*-algebras. Chapter 4 offers the classification of the so-called AT-algebras of real rank zero. The first four chapters are self-contained, and can serve as a text for a graduate course on C*-algebras. The last two chapters contain more advanced material. In particular, they deal with the classification theorem for simple AH-algebras with real rank zero, the work of Elliott and Gong. The book contains many new proofs and some original results related to the classification of amenable C*-algebras. As well as providing an introduction to the theory of the classification of amenable C*-algebras, it is a comprehensive reference for those more familiar with the subject C*-algèbres K-théorie MATHEMATICS / Algebra / Linear bisacsh C*-algebras fast K-theory fast C*-algebra's gtt Análise funcional larpcal C* álgebras larpcal C*-algebras K-theory C-Stern-Algebra (DE-588)4136693-1 gnd rswk-swf Klassifikation (DE-588)4030958-7 gnd rswk-swf C-Stern-Algebra (DE-588)4136693-1 s Klassifikation (DE-588)4030958-7 s 1\p DE-604 http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=235800 Aggregator Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Lin, Huaxin An introduction to the classification of amenable C*-algebras C*-algèbres K-théorie MATHEMATICS / Algebra / Linear bisacsh C*-algebras fast K-theory fast C*-algebra's gtt Análise funcional larpcal C* álgebras larpcal C*-algebras K-theory C-Stern-Algebra (DE-588)4136693-1 gnd Klassifikation (DE-588)4030958-7 gnd |
| subject_GND | (DE-588)4136693-1 (DE-588)4030958-7 |
| title | An introduction to the classification of amenable C*-algebras |
| title_alt | Amenable C*-algebras |
| title_auth | An introduction to the classification of amenable C*-algebras |
| title_exact_search | An introduction to the classification of amenable C*-algebras |
| title_full | An introduction to the classification of amenable C*-algebras Huaxin Lin |
| title_fullStr | An introduction to the classification of amenable C*-algebras Huaxin Lin |
| title_full_unstemmed | An introduction to the classification of amenable C*-algebras Huaxin Lin |
| title_short | An introduction to the classification of amenable C*-algebras |
| title_sort | an introduction to the classification of amenable c algebras |
| topic | C*-algèbres K-théorie MATHEMATICS / Algebra / Linear bisacsh C*-algebras fast K-theory fast C*-algebra's gtt Análise funcional larpcal C* álgebras larpcal C*-algebras K-theory C-Stern-Algebra (DE-588)4136693-1 gnd Klassifikation (DE-588)4030958-7 gnd |
| topic_facet | C*-algèbres K-théorie MATHEMATICS / Algebra / Linear C*-algebras K-theory C*-algebra's Análise funcional C* álgebras C-Stern-Algebra Klassifikation |
| url | http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=235800 |
| work_keys_str_mv | AT linhuaxin anintroductiontotheclassificationofamenablecalgebras AT linhuaxin amenablecalgebras |