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: | |
| Links: | 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 |
| Physical Description: | XVIII, 239 Seiten |
| ISBN: | 9783037191286 |
Staff View
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Record in the Search Index
| _version_ | 1819317712517595136 |
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| adam_text | 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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| discipline | Mathematik |
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| indexdate | 2024-12-20T16:50:00Z |
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| isbn | 9783037191286 |
| language | English |
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| physical | XVIII, 239 Seiten |
| publishDate | 2013 |
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| 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 |
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