Essays in the history of lie groups and algebraic groups:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, RI
American Mathematical Society
2001
|
| Schriftenreihe: | History of mathematics
21 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIII, 184 S. Ill. |
| ISBN: | 0821802887 |
Internformat
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| 245 | 1 | 0 | |a Essays in the history of lie groups and algebraic groups |c Armand Borel |
| 264 | 1 | |a Providence, RI |b American Mathematical Society |c 2001 | |
| 300 | |a XIII, 184 S. |b Ill. | ||
| 336 | |b txt |2 rdacontent | ||
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| 490 | 1 | |a History of mathematics |v 21 | |
| 648 | 7 | |a Geschichte 1900-2000 |2 gnd |9 rswk-swf | |
| 650 | 7 | |a Algebraïsche groepen |2 gtt | |
| 650 | 7 | |a Groupe de Lie |2 rasuqam | |
| 650 | 7 | |a Groupe linéaire algébrique |2 rasuqam | |
| 650 | 4 | |a Groupes linéaires algébriques - Histoire | |
| 650 | 7 | |a Histoire |2 rasuqam | |
| 650 | 4 | |a Lie, Groupes de - Histoire | |
| 650 | 7 | |a Lie-groepen |2 gtt | |
| 650 | 4 | |a Geschichte | |
| 650 | 4 | |a Lie groups |x History | |
| 650 | 4 | |a Linear algebraic groups |x History | |
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| 689 | 1 | 1 | |a Geschichte 1900-2000 |A z |
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Datensatz im Suchindex
| _version_ | 1804128713220030464 |
|---|---|
| adam_text | Contents
Introduction ix
Terminology for Classical Groups and Notation xi
Photo Credits xiii
Chapter I. Overview 1
§1. Lie s theory 1
§2. Lie algebras 5
§3. Globalizations 6
References for Chapter I 8
Chapter II. Full Reducibility and Invariants for SL2(C) 9
§1. Full reducibility, 1890 96 9
§2. Averaging. The invariant theorem 11
§3. Algebraic proofs of full reducibility 16
§4. Appendix: More on some proofs of full reducibility 18
References for Chapter II 26
Chapter III. Hermann Weyl and Lie Groups 29
§1. First contacts with Lie groups 29
§2. Representations of semisimple Lie groups and Lie algebras 31
§3. Impact on E. Cartan 35
§4. The Peter Weyl theorem. Harmonic analysis 37
§5. Group theory and quantum mechanics 38
§6. Representations and invariants of classical groups 40
§7. Two later developments 44
Notes 46
References for Chapter III 54
Chapter IV. Elie Cartan, Symmetric Spaces and Lie Groups 59
A. Building Up the Theory 60
§1. The spaces £. Local theory 60
§2. Spaces £ and semisimple groups. Global theory 64
§3. An exposition of Lie group theory from the global point of view 79
B. Further Developments 80
§4. Complete orthogonal systems on homogeneous spaces of compact
Lie groups 80
viii CONTENTS
§5. Differential forms and algebraic topology 84
§6. Bounded symmetric domains 88
References for Chapter IV 90
Chapter V. Linear Algebraic Groups in the 19th Century 93
§1. S. Lie, E. Study, and projective representations 93
§2. E. Study, Gordan series and linear representations of SL3 97
§3. Emile Picard 99
§4. Ludwig Maurer 102
§5. Elie Cartan 114
§6. Karl Carda 115
References for Chapter V 117
Chapter VI. Linear Algebraic Groups in the 20th Century 119
§1. Linear algebraic groups in characteristic zero. Replicas 119
§2. Groups over algebraically closed ground fields I 119
§3. Groups over an algebraically closed ground field II 124
§4. Rationality properties 126
§5. Algebraic groups and geometry. Tits systems and Tits buildings 131
§6. Abstract automorphisms 134
§7. Merger 142
References for Chapter VI 144
Chapter VII. The Work of Chevalley in Lie Groups and Algebraic Groups 147
§1. Lie groups, 1941 1946 147
§2. Linear algebraic groups, 1943 1951 150
§3. Lie groups, 1948 1955 152
§4. Linear algebraic groups, 1954 155
§5. Algebraic groups. 1955 1961 156
References for Chapter VII 162
Chapter VIII. Algebraic Groups and Galois Theory in the Work of Ellis R.
Kolchin 165
§1. The Picard Vessiot theory 165
§2. Linear algebraic groups 169
§3. Generalization of the Picard Vessiot theory 170
§4. Galois theory of strongly normal extensions 173
§5. Foundational work on algebraic sets and groups 176
References for Chapter VIII 179
Name Index 181
Subject Index 183
|
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| era | Geschichte 1900-2000 gnd |
| era_facet | Geschichte 1900-2000 |
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| indexdate | 2024-07-09T18:53:37Z |
| institution | BVB |
| isbn | 0821802887 |
| language | English |
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| physical | XIII, 184 S. Ill. |
| publishDate | 2001 |
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| series | History of mathematics |
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| spelling | Borel, Armand 1923-2003 Verfasser (DE-588)119089106 aut Essays in the history of lie groups and algebraic groups Armand Borel Providence, RI American Mathematical Society 2001 XIII, 184 S. Ill. txt rdacontent n rdamedia nc rdacarrier History of mathematics 21 Geschichte 1900-2000 gnd rswk-swf Algebraïsche groepen gtt Groupe de Lie rasuqam Groupe linéaire algébrique rasuqam Groupes linéaires algébriques - Histoire Histoire rasuqam Lie, Groupes de - Histoire Lie-groepen gtt Geschichte Lie groups History Linear algebraic groups History Lineare algebraische Gruppe (DE-588)4295326-1 gnd rswk-swf Lie-Gruppe (DE-588)4035695-4 gnd rswk-swf Lie-Gruppe (DE-588)4035695-4 s Geschichte 1900-2000 z DE-604 Lineare algebraische Gruppe (DE-588)4295326-1 s Erscheint auch als Online-Ausgabe 978-1-4704-3889-0 History of mathematics 21 (DE-604)BV001327576 21 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009492671&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Borel, Armand 1923-2003 Essays in the history of lie groups and algebraic groups History of mathematics Algebraïsche groepen gtt Groupe de Lie rasuqam Groupe linéaire algébrique rasuqam Groupes linéaires algébriques - Histoire Histoire rasuqam Lie, Groupes de - Histoire Lie-groepen gtt Geschichte Lie groups History Linear algebraic groups History Lineare algebraische Gruppe (DE-588)4295326-1 gnd Lie-Gruppe (DE-588)4035695-4 gnd |
| subject_GND | (DE-588)4295326-1 (DE-588)4035695-4 |
| title | Essays in the history of lie groups and algebraic groups |
| title_auth | Essays in the history of lie groups and algebraic groups |
| title_exact_search | Essays in the history of lie groups and algebraic groups |
| title_full | Essays in the history of lie groups and algebraic groups Armand Borel |
| title_fullStr | Essays in the history of lie groups and algebraic groups Armand Borel |
| title_full_unstemmed | Essays in the history of lie groups and algebraic groups Armand Borel |
| title_short | Essays in the history of lie groups and algebraic groups |
| title_sort | essays in the history of lie groups and algebraic groups |
| topic | Algebraïsche groepen gtt Groupe de Lie rasuqam Groupe linéaire algébrique rasuqam Groupes linéaires algébriques - Histoire Histoire rasuqam Lie, Groupes de - Histoire Lie-groepen gtt Geschichte Lie groups History Linear algebraic groups History Lineare algebraische Gruppe (DE-588)4295326-1 gnd Lie-Gruppe (DE-588)4035695-4 gnd |
| topic_facet | Algebraïsche groepen Groupe de Lie Groupe linéaire algébrique Groupes linéaires algébriques - Histoire Histoire Lie, Groupes de - Histoire Lie-groepen Geschichte Lie groups History Linear algebraic groups History Lineare algebraische Gruppe Lie-Gruppe |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009492671&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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