Basic noncommutative geometry:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Zürich
European Mathematical Society
[2013]
|
| Edition: | Second edition |
| Series: | EMS series of lectures in mathematics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVIII, 239 Seiten |
| ISBN: | 9783037191286 |
Staff View
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Record in the Search Index
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Titel: Basic noncommutative geometry
Autor: Khalkhali, Masoud
Jahr: 2013
Contents
Preface to the second edition vii
Introduction xi
1 Examples of algebra-geometry correspondences 1
1.1 Locally compact spaces and commutative C *-algebras. 1
1.1.1 The spectrum. 2
1.1.2 The Gelfand transform. 3
1.1.3 Noncommutative spaces. 7
1.1.4 Noncommutative spaces from groups. 9
1.1.5 Noncommutative tori. 14
1.2 Vector bundles, finite projective modules, and idempotents. 18
1.3 Affine varieties and finitely generated commutative reduced algebras . 24
1.4 Affine schemes and commutative rings. 26
1.5 Compact Riemann surfaces and algebraic function fields. 28
1.6 Sets and Boolean algebras . 29
1.7 From groups to Hopf algebras and quantum groups. 30
1.7.1 Symmetry in noncommutative geometry . 39
2 Noncommutative quotients 47
2.1 Groupoids. 47
2.2 Groupoid algebras. 52
2.3 Morita equivalence. 64
2.4 Morita equivalence for C*-algebras. 73
2.5 Noncommutative quotients. 79
2.6 Sources of noncommutative spaces. 86
3 Cyclic cohomology 87
3.1 Hochschild cohomology . 89
3.2 Hochschild cohomology as a derived functor. 95
3.3 Deformation theory. 102
3.4 Topological algebras . 112
3.5 Examples: Hochschild (co)homology . 115
3.6 Cyclic cohomology. 124
3.7 Connes' long exact sequence. 136
3.8 Connes' spectral sequence . 140
3.9 Cyclic modules. 143
3.10 Examples: cyclic cohomology. 148
Contents
3.11 Hopf cyclic cohomology. 154
4 Connes-Chern character 163
4.1 Connes-Chern character in K-theory. 163
4.1.1 Basic ^-theory. 164
4.1.2 Pairing with cyclic cohomology. 166
4.1.3 Noncommutative Chern-Weil theory. 172
4.1.4 The Gauss-Bonnet theorem and scalar curvature in
noncommutative geometry. 176
4.2 Connes-Chern character in ^-homology. 177
4.3 Algebras stable under holomorphic functional calculus. 194
4.4 A final word: basic noncommutative geometry in a nutshell. 199
Appendices 201
A Gelfand-Naimark theorems 201
A.l Gelfand's theory of commutative Banach algebras. 201
A.2 States and the GNS construction. 205
B Compact operators, Fredholm operators, and abstract index theory 212
C Projective modules 219
D Equivalence of categories 221
Bibliography 223
Index 235 |
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| isbn | 9783037191286 |
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| spelling | Khalkhali, Masoud 1963- Verfasser (DE-588)136619029 aut Basic noncommutative geometry Masoud Khalkhali Second edition Zürich European Mathematical Society [2013] © 2013 XVIII, 239 Seiten txt rdacontent n rdamedia nc rdacarrier EMS series of lectures in mathematics Nichtkommutative Geometrie (DE-588)4171742-9 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Nichtkommutative Geometrie (DE-588)4171742-9 s DE-604 Erscheint auch als Online-Ausgabe 978-3-03719-628-1 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027035593&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Khalkhali, Masoud 1963- Basic noncommutative geometry Nichtkommutative Geometrie (DE-588)4171742-9 gnd |
| subject_GND | (DE-588)4171742-9 (DE-588)4123623-3 |
| title | Basic noncommutative geometry |
| title_auth | Basic noncommutative geometry |
| title_exact_search | Basic noncommutative geometry |
| title_full | Basic noncommutative geometry Masoud Khalkhali |
| title_fullStr | Basic noncommutative geometry Masoud Khalkhali |
| title_full_unstemmed | Basic noncommutative geometry Masoud Khalkhali |
| title_short | Basic noncommutative geometry |
| title_sort | basic noncommutative geometry |
| topic | Nichtkommutative Geometrie (DE-588)4171742-9 gnd |
| topic_facet | Nichtkommutative Geometrie Lehrbuch |
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