Stable modules and the D(2)-problem
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge, UK
Cambridge Univ. Pr.
2003
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| Schriftenreihe: | London Mathematical Society lecture note series
301 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
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| 100 | 1 | |a Johnson, Francis Edward Anthony |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Stable modules and the D(2)-problem |c F.E.A. Johnson |
| 264 | 1 | |a Cambridge, UK |b Cambridge Univ. Pr. |c 2003 | |
| 300 | |a ix, 267 S. | ||
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Datensatz im Suchindex
| DE-BY-TUM_call_number | 0102 MAT 001z 2001 A 985 |
|---|---|
| DE-BY-TUM_katkey | 1515298 |
| DE-BY-TUM_location | 01 |
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| _version_ | 1820796142120599552 |
| adam_text | Contents
Acknowledgements page x
Introduction 1
1 Orders in semisimple algebras 13
1 Simple algebras 13
2 Semisimple modules 17
3 Projective modules and semisimplicity 21
4 The Jacobson radical 23
5 Nondegenerate algebras 26
6 The discriminant 28
7 Z orders 30
8 Examples 33
2 Representation theory of finite groups 38
9 Group representations 38
10 Maschke s Theorem 40
11 Division algebras over Q 42
12 Examples of Wedderburn decompositions 45
3 Stable modules and cancellation theorems 52
13 Schanuel s Lemma 52
14 The structure of stable modules 53
15 The Swan Jacobinski Theorem 56
16 Finitenessof AT0(Z[G]) 59
17 Non cancellation and an example of Swan 60
18 Non cancellation over group rings 64
4 Relative homological algebra 67
19 The derived category of a tame class 68
20 Derived functors 74
21 The long exact sequence in cohomology 78
22 Stable modules and the derived category 83
vii
viii Contents
23 Module extensions and Ext1 87
24 General module extensions and Ext 94
25 Classification of general module extensions 98
26 Classification of projective n stems 104
27 The standard cohomology theory of modules 108
5 The derived category of a finite group 114
28 Lattices over a finite group 114
29 The stable modules Qn(Z) 120
30 Stably free extensions 122
31 Subgroup relations in the derived category 125
32 Restriction and transfer 129
6 ^ invariants 132
33 Endomorphisms in the derived category 132
34 fc invariants and the action of Autuer(^) 135
35 Qi(Z)andfi_,(Z) 137
36 Swan modules 139
37 Swan s isomorphism criterion 141
38 Congruence classes and Swan modules 146
39 The Tate ring 148
7 Groups of periodic cohomology 151
40 Periodicity conditions 151
41 Examples 154
42 Subgroup structure at odd primes 156
43 Subgroup structure at the prime 2 159
44 The Artin Tate Theorem 161
45 The Zassenhaus Suzuki classification 164
8 Algebraic homotopy theory 171
46 Chain complexes, homotopy and homology 172
47 Two dimensional complexes 180
48 Cayley complexes 183
49 Algebraicity of two dimensional homotopy 187
9 Stability theorems 193
50 Algebraic stabilization 194
51 Stable isomorphism of stably free extensions 197
52 Eventual stability of homotopy types 200
53 The Swan map 203
54 Module automorphisms and ^ invariants 210
55 Realization Theorems 213
56 Augmentation sequences 216
57 Classification over groups of period 4 220
Contents ix
10 The D(2) problem 224
58 Cohomologically two dimensional 3 complexes 224
59 The virtual 2 complex 227
60 Reduction to two dimensional data 229
61 Group presentations and fi3(Z) 232
62 Verifying the D(2) property 234
11 Poincare 3 complexes 239
63 Attaching 3 cells to a presentation 240
64 Another characterization of groups of period 4 243
65 Poincare 3 complexes of standard form 245
66 Relationship with the D(2) problem 247
67 Terminus: the limits of this book 249
Appendix A The D(2) property for free groups 252
Appendix B The Realization Theorem 256
References 262
Index 266
|
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| id | DE-604.BV019883406 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-23T18:18:16Z |
| institution | BVB |
| isbn | 0521537495 |
| language | English |
| lccn | 2003046133 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-013207517 |
| oclc_num | 51886466 |
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| owner | DE-91G DE-BY-TUM DE-355 DE-BY-UBR DE-11 |
| owner_facet | DE-91G DE-BY-TUM DE-355 DE-BY-UBR DE-11 |
| physical | ix, 267 S. |
| publishDate | 2003 |
| publishDateSearch | 2003 |
| publishDateSort | 2003 |
| publisher | Cambridge Univ. Pr. |
| record_format | marc |
| series | London Mathematical Society lecture note series |
| series2 | London Mathematical Society lecture note series |
| spellingShingle | Johnson, Francis Edward Anthony Stable modules and the D(2)-problem London Mathematical Society lecture note series Grupos finitos larpcal Álgebra larpcal Low-dimensional topology Homotopy theory Group algebras Gruppenring (DE-588)4158469-7 gnd Homotopietheorie (DE-588)4128142-1 gnd Niederdimensionale Topologie (DE-588)4280826-1 gnd |
| subject_GND | (DE-588)4158469-7 (DE-588)4128142-1 (DE-588)4280826-1 |
| title | Stable modules and the D(2)-problem |
| title_auth | Stable modules and the D(2)-problem |
| title_exact_search | Stable modules and the D(2)-problem |
| title_full | Stable modules and the D(2)-problem F.E.A. Johnson |
| title_fullStr | Stable modules and the D(2)-problem F.E.A. Johnson |
| title_full_unstemmed | Stable modules and the D(2)-problem F.E.A. Johnson |
| title_short | Stable modules and the D(2)-problem |
| title_sort | stable modules and the d 2 problem |
| topic | Grupos finitos larpcal Álgebra larpcal Low-dimensional topology Homotopy theory Group algebras Gruppenring (DE-588)4158469-7 gnd Homotopietheorie (DE-588)4128142-1 gnd Niederdimensionale Topologie (DE-588)4280826-1 gnd |
| topic_facet | Grupos finitos Álgebra Low-dimensional topology Homotopy theory Group algebras Gruppenring Homotopietheorie Niederdimensionale Topologie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013207517&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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| work_keys_str_mv | AT johnsonfrancisedwardanthony stablemodulesandthed2problem |