Cyclic homology:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin ; Heidelberg
Springer
[1998]
|
| Edition: | Second edition |
| Series: | Die Grundlehren der mathematischen Wissenschaften
301 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverzeichnis: Seite 431 - 444 |
| Physical Description: | xviii, 513 Seiten Illustrationen, Diagramme |
| ISBN: | 3540630740 9783540630746 9783642083167 |
Staff View
MARC
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| 245 | 1 | 0 | |a Cyclic homology |c Jean-Louis Loday |
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Record in the Search Index
| _version_ | 1804125950234853376 |
|---|---|
| adam_text | Contents
Introduction XV
Notation and Terminology XIX
Chapter 1. Hochschild Homology 1
1.0 Chain Complexes 2
1.1 Hochschild Homology 8
1.2 The Trace Map and Morita Invariance Hi
1.3 Derivations, Differential Forms 23
1.4 Nonunital Algebras and Excision 29
1.5 Hochschild Cohomology, Cotrace, Duality 37
1.6 Simplicial Modules 44
Bibliographical Comments on Chapter 1 48
Chapter 2. Cyclic Homology of Algebras 51
2.1 Definition of Cyclic Homology 53
2.2 Connes Exact Sequence, Morita Invariance. Excision 61
2.3 Differential Forms, de Rham Cohomology 68
2.4 Cyclic Cohomology 72
2.5 Cyclic Modules 75
2.6 Non commutative Differential Forms 83
Bibliographical Comments on Chapter 2 88
Chapter 3. Smooth Algebras and Other Examples 89
3.1 Tensor Algebra 90
3.2 Symmetric Algebras 94
3.3 Universal Enveloping Algebras of Lie Algebras 97
3.4 Smooth Algebras 101
3.5 Andre Quillen Homology 107
3.6 Deligne Cohomology 112
Bibliographical Comments on Chapter 3 Ill
XII Contents
Chapter 4. Operations on Hochschild and Cyclic Homology . 115
4.1 Conjugation and Derivation 116
4.2 Shuffle Product in Hochschild Homology 123
4.3 Cyclic Shuffles and Kiinneth Sequence for HC 127
4.4 Product, Coproduct in Cyclic Homology 133
4.5 A Decomposition for Hochschild Homology 139
4.6 A Decomposition for Cyclic Homology 149
Bibliographical Comments on Chapter 4 155
Chapter 5. Variations on Cyclic Homology 157
5.1 The Periodic and Negative Theories 158
5.2 Dihedral and Quaternionic Homology 167
5.3 Differential Graded Algebras 175
5.4 Commutative Differential Graded Algebras 182
5.5 Bivariant Cyclic Cohomology 190
5.6 Topological Algebras, Entire Cyclic Cohomology 195
Bibliographical Comments on Chapter 5 199
Chapter 6. The Cyclic Category, Tor and Ext Interpretation 201
6.1 Connes Cyclic Category AC and the Category AS 202
6.2 Tor and Ext Interpretation of HH and HC 211
6.3 Crossed Simplicial Groups 214
6.4 The Category of Finite Sets and the A Decomposition 220
Bibliographical Comments on Chapter 6 225
Chapter 7. Cyclic Spaces and S 1 Equivariant Homology .... 227
7.1 Cyclic Sets and Cyclic Spaces 228
7.2 Cyclic Homology and S : Equivariant Homology 234
7.3 Examples of Cyclic Sets and the Free Loop Space 241
7.4 Hochschild Homology and Cyclic Homology of Group
Algebras 250
Bibliographical Comments on Chapter 7 256
Chapter 8. Chern Character 257
8.1 The Classical Chern Character a la Chern Weil 258
8.2 The Grothendieck Group KQ 261
8.3 The Chern Character from Ko to Cyclic Homology 264
8.4 The Dennis Trace Map and the Generalized Chern Character . . 269
8.5 The Bass Trace Conjecture and the Idempotent Conjecture .... 277
Bibliographical Comments on Chapter 8 279
Contents XIII
Chapter 9. Classical Invariant Theory 281
9.1 The Fundamental Theorems of Invariant Theory 282
9.2 Coinvariant Theory and the Trace Map 284
9.3 Cayley Hamilton and Amitsur Levitzki Formulas 287
9.4 Proofs of the Fundamental Theorems 291
9.5 Invariant Theory for the Orthogonal and Symplectic Groups . . . 293
Bibliographical Comments on Chapter 9 297
Chapter 10. Homology of Lie Algebras of Matrices 299
10.1 Homology of Lie Algebras 301
10.2 Homology of the Lie Algebra gl(A) 306
10.3 Stability and First Obstruction to Stability 315
10.4 Homology with Coefficients in the Adjoint Representation ..... 320
10.5 The Symplectic and Orthogonal Cases 323
10.6 Non commutative Homology (or Leibniz Homology)
of the Lie Algebra of Matrices 326
Bibliographical Comments on Chapter 10 340
Chapter 11. Algebraic K Theory 341
11.1 The Bass Whitehead Group Kx and the Milnor Group K2 ¦ ... 342
11.2 Higher Algebraic tf Theory 349
11.3 Algebraic K Theory and Cyclic Homology of Nilpot.ent Ideals . . 361
11.4 Absolute and Relative Chern Characters 371
11.5 Secondary Characteristic Classes 375
Bibliographical Comments on Chapter 11 379
Chapter 12. Non commutative Differential Geometry ....... 381
12.1 Foliations and the Godbillon Vey Invariant 382
12.2 Fredholm Modules and Index Theorems 385
12.3 Novikov Conjecture on Higher Signatures 390
12.4 The A Theoretic Analogue of the Novikov Conjecture 395
Chapter 13. Mac Lane (co)homology 399
by Jean Louis Loday and Teimuraz Pirashvili
13.1 (Co)homology with Coefficients in Non additive Bimodules .... 401
13.2 Mac Lane (co)homology 408
13.3 Stable K theory and Mac Lane homology 417
13.4 Calculations 428
Bibliographical Comments on Chapter 13 142
References of Chapter 13 443
XIV Contents
Appendices
A. Hopf Algebras 447
B. Simplicial 453
C. Homology of Discrete Groups and Small Categories 461
D. Spectral Sequences 469
E. Smooth Algebras 473
References 485
References 1992 1996 499
Symbols 509
Index 511
|
| any_adam_object | 1 |
| author | Loday, Jean-Louis 1946-2012 |
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| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.55 |
| dewey-search | 512/.55 |
| dewey-sort | 3512 255 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | Second edition |
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| id | DE-604.BV011434358 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:09:42Z |
| institution | BVB |
| isbn | 3540630740 9783540630746 9783642083167 |
| language | English |
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| physical | xviii, 513 Seiten Illustrationen, Diagramme |
| publishDate | 1998 |
| publishDateSearch | 1998 |
| publishDateSort | 1998 |
| publisher | Springer |
| record_format | marc |
| series | Die Grundlehren der mathematischen Wissenschaften |
| series2 | Die Grundlehren der mathematischen Wissenschaften |
| spelling | Loday, Jean-Louis 1946-2012 Verfasser (DE-588)122970756 aut Cyclic homology Jean-Louis Loday Second edition Berlin ; Heidelberg Springer [1998] © 1998 xviii, 513 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Die Grundlehren der mathematischen Wissenschaften 301 Literaturverzeichnis: Seite 431 - 444 Homologie ram Homology theory Homologietheorie (DE-588)4141714-8 gnd rswk-swf Zyklische Homologie (DE-588)4269326-3 gnd rswk-swf Zyklische Homologie (DE-588)4269326-3 s DE-604 Homologietheorie (DE-588)4141714-8 s 1\p DE-604 Erscheint auch als Online-Ausgabe 978-3-662-11389-9 Die Grundlehren der mathematischen Wissenschaften 301 (DE-604)BV000000395 301 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007689733&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Loday, Jean-Louis 1946-2012 Cyclic homology Die Grundlehren der mathematischen Wissenschaften Homologie ram Homology theory Homologietheorie (DE-588)4141714-8 gnd Zyklische Homologie (DE-588)4269326-3 gnd |
| subject_GND | (DE-588)4141714-8 (DE-588)4269326-3 |
| title | Cyclic homology |
| title_auth | Cyclic homology |
| title_exact_search | Cyclic homology |
| title_full | Cyclic homology Jean-Louis Loday |
| title_fullStr | Cyclic homology Jean-Louis Loday |
| title_full_unstemmed | Cyclic homology Jean-Louis Loday |
| title_short | Cyclic homology |
| title_sort | cyclic homology |
| topic | Homologie ram Homology theory Homologietheorie (DE-588)4141714-8 gnd Zyklische Homologie (DE-588)4269326-3 gnd |
| topic_facet | Homologie Homology theory Homologietheorie Zyklische Homologie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007689733&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000395 |
| work_keys_str_mv | AT lodayjeanlouis cyclichomology |