Tensor products and regularity properties of Cuntz semigroups:
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, Rhode Island
American Mathematical Society
January 2018
|
| Series: | Memoirs of the American Mathematical Society
volume 251, number 1199 (sixth of 6 numbers) |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | viii, 191, 4 ungezählte Seiten |
| ISBN: | 9781470427979 |
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MARC
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Record in the Search Index
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| adam_text | Contents
Chapter 1. Introduction 1
1.1. Background 1
1.2. The categories W and Cu 4
1.3. Tensor products 7
1.4. Multiplicative structure of Cu-semigroups. Solid Cu-semirings 8
Acknowledgments 10
Chapter 2. Pre-completed Cuntz semigroups 11
2.1. The categories PreW and W 11
2.2. The pre-completed Cuntz semigroup of a C*-algebra 16
Chapter 3. Completed Cuntz semigroups 21
3.1. The category Cu 21
3.2. The completed Cuntz semigroup of a C*-algebra 27
Chapter 4. Additional axioms 31
Chapter 5. Structure of Cu-semigroups 37
5.1. Ideals and quotients 37
5.2. Functionals 45
5.3. Soft and purely noncompact elements 56
5.4. Predecessors, after Engbers 64
5.5. Algebraic semigroups 67
5.6. Nearly unperforated semigroups 72
Chapter 6. Bimorphisms and tensor products 81
6.1. Tensor product as representing object 82
6.2. The tensor product in PreW 85
6.3. The tensor product in Cu 94
6.4. Examples and Applications 96
Chapter 7. Cu-semirings and Cu-semimodules 105
7.1. Strongly self-absorbing C*-algebras and solid Cu-semirings 107
7.2. Cuntz semigroups of purely infinite C*-algebras 113
7.3. Almost unperforated and almost divisible Cu-semigroups 118
7.4. The rationalization of a semigroup 126
7.5. The realification of a semigroup 132
7.6. Examples and Applications 136
Chapter 8. Structure of Cu-semirings 139
8.1. Simple Cu-semirings 139
V
Vi
CONTENTS
8.2. Algebraic Cu-semirings 146
8.3. Classification of solid Cu-semirings 149
Chapter 9. Concluding remarks and open problems 159
Appendix A. Monoidal and enriched categories 163
Appendix B. Partially ordered monoids, groups and rings 167
B.l. The category Mon of monoids 167
B.2. The categories PrePOM and POM 172
B.3. The category POGp of partially ordered groups 176
B.4. The category PORg of partially ordered rings 178
Bibliography 181
Index of Terms 187
Index of Symbols 191
|
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| id | DE-604.BV044868790 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T08:03:20Z |
| institution | BVB |
| isbn | 9781470427979 |
| language | English |
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| physical | viii, 191, 4 ungezählte Seiten |
| publishDate | 2018 |
| publishDateSearch | 2018 |
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| publisher | American Mathematical Society |
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| series | Memoirs of the American Mathematical Society |
| series2 | Memoirs of the American Mathematical Society |
| spelling | Antoine, Ramon 1973- (DE-588)1131742133 aut Tensor products and regularity properties of Cuntz semigroups Ramon Antoine ; Francesc Perera ; Hannes Thiel Providence, Rhode Island American Mathematical Society January 2018 viii, 191, 4 ungezählte Seiten txt rdacontent n rdamedia nc rdacarrier Memoirs of the American Mathematical Society volume 251, number 1199 (sixth of 6 numbers) Perera, Francesc aut Thiel, Hannes (DE-588)1131742737 aut Memoirs of the American Mathematical Society volume 251, number 1199 (sixth of 6 numbers) (DE-604)BV008000141 1199 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=030263276&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Antoine, Ramon 1973- Perera, Francesc Thiel, Hannes Tensor products and regularity properties of Cuntz semigroups Memoirs of the American Mathematical Society |
| title | Tensor products and regularity properties of Cuntz semigroups |
| title_auth | Tensor products and regularity properties of Cuntz semigroups |
| title_exact_search | Tensor products and regularity properties of Cuntz semigroups |
| title_full | Tensor products and regularity properties of Cuntz semigroups Ramon Antoine ; Francesc Perera ; Hannes Thiel |
| title_fullStr | Tensor products and regularity properties of Cuntz semigroups Ramon Antoine ; Francesc Perera ; Hannes Thiel |
| title_full_unstemmed | Tensor products and regularity properties of Cuntz semigroups Ramon Antoine ; Francesc Perera ; Hannes Thiel |
| title_short | Tensor products and regularity properties of Cuntz semigroups |
| title_sort | tensor products and regularity properties of cuntz semigroups |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030263276&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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