From the basic homotopy lemma to the classification of C*-algebras:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, Rhode Island
American Mathematical Society
[2017]
|
| Series: | Regional conference series in mathematics
number 124 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | vi, 240 Seiten |
| ISBN: | 9781470434908 |
Staff View
MARC
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Record in the Search Index
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| adam_text | Contents
Preface v
Chapter 0. An overview of the Elliott program 1
Chapter 1. An introduction to the Basic Homotopy Lemma 7
1.1. A taste of the Basic Homotopy Lemma 7
1.2. Some easy applications 9
1.3. The Voiculescu example and an Exel-Loring invariant 15
1.4. Exercises 18
Chapter 2. Maps to finite dimensional £7*-algebras 21
2.1. Preliminaries 21
2.2. Homogeneous CP-algebras 28
2.3. Subhomogeneous C^-algebras 35
2.4. Exercises 48
Chapter 3. Stable Homotopy Lemmas 51
3.1. Stable uniqueness theorems 51
3.2. Stable homotopy 56
3.3. The Bott map revisited 60
3.4. Exercises 70
Chapter 4. The Basic Homotopy Lemma, finite dimensional cases 73
4.1. Two uniqueness theorems 73
4.2. Real rank zero and quasidiagonal extensions 80
4.3. Almost multiplicative maps 83
4.4. Basic Homotopy Lemma in finite dimensional CP-algebras 89
4.5. An existence theorem for Bott maps 96
4.6. Exercises 107
Chapter 5. C*-algebras of generalized tracial rank one 109
5.1. Elliott-Thomsen building blocks 109
5.2. A uniqueness theorem for subhomogeneous C*-algebras 117
5.3. Cf*-algebras with gTR{A) 1 129
5.4. A uniqueness theorem for C*-algebras with gTR(A) 1 139
5.5. The range theorem and the isomorphism theorem 149
5.6. Exercises 154
Chapter 6. More Basic Homotopy Lemmas 157
6.1. Pairs of almost commuting unitàries 157
6.2. More existence theorems related to the Bott map 161
iii
IV
CONTENTS
6.3. The Basic Homotopy Lemma in Bq 168
6.4. K K-liit mg 174
6.5. Exercises 187
Chapter 7. Asymptotic unitary equivalence 189
7.1. The rotation map 189
7.2. Introduction of asymptotic unitary equivalence 194
7.3. A uniqueness theorem for asymptotic unitary equivalence 198
7.4. The range of asymptotic unitary equivalence classes 205
7.5. Exercises 212
Chapter 8. Classification of simple C*-algebras of finite rank 215
8.1. Strong asymptotic unitary equivalence 215
8.2. The Jiang-Su algebra and Winter’s deformation 217
8.3. The classification theorem 225
8.4. Non-unital cases 228
Bibliography 283
Index 239
|
| any_adam_object | 1 |
| author | Lin, Huaxin 1956- |
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| author_facet | Lin, Huaxin 1956- |
| author_role | aut |
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| dewey-full | 511.6 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.6 |
| dewey-search | 511.6 |
| dewey-sort | 3511.6 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV044538128 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:55:20Z |
| institution | BVB |
| isbn | 9781470434908 |
| language | English |
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| physical | vi, 240 Seiten |
| publishDate | 2017 |
| publishDateSearch | 2017 |
| publishDateSort | 2017 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | Regional conference series in mathematics |
| series2 | Regional conference series in mathematics |
| spelling | Lin, Huaxin 1956- Verfasser (DE-588)141411228 aut From the basic homotopy lemma to the classification of C*-algebras Huaxin Lin Providence, Rhode Island American Mathematical Society [2017] © 2017 vi, 240 Seiten txt rdacontent n rdamedia nc rdacarrier Regional conference series in mathematics number 124 C-Stern-Algebra (DE-588)4136693-1 gnd rswk-swf Rationale Homotopietheorie (DE-588)4177003-1 gnd rswk-swf Rationale Homotopietheorie (DE-588)4177003-1 s C-Stern-Algebra (DE-588)4136693-1 s DE-604 Regional conference series in mathematics number 124 (DE-604)BV000004346 124 Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029937262&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lin, Huaxin 1956- From the basic homotopy lemma to the classification of C*-algebras Regional conference series in mathematics C-Stern-Algebra (DE-588)4136693-1 gnd Rationale Homotopietheorie (DE-588)4177003-1 gnd |
| subject_GND | (DE-588)4136693-1 (DE-588)4177003-1 |
| title | From the basic homotopy lemma to the classification of C*-algebras |
| title_auth | From the basic homotopy lemma to the classification of C*-algebras |
| title_exact_search | From the basic homotopy lemma to the classification of C*-algebras |
| title_full | From the basic homotopy lemma to the classification of C*-algebras Huaxin Lin |
| title_fullStr | From the basic homotopy lemma to the classification of C*-algebras Huaxin Lin |
| title_full_unstemmed | From the basic homotopy lemma to the classification of C*-algebras Huaxin Lin |
| title_short | From the basic homotopy lemma to the classification of C*-algebras |
| title_sort | from the basic homotopy lemma to the classification of c algebras |
| topic | C-Stern-Algebra (DE-588)4136693-1 gnd Rationale Homotopietheorie (DE-588)4177003-1 gnd |
| topic_facet | C-Stern-Algebra Rationale Homotopietheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029937262&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000004346 |
| work_keys_str_mv | AT linhuaxin fromthebasichomotopylemmatotheclassificationofcalgebras |