Introduction to Lie groups and transformation groups:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin, [u.a.]
Springer
1969
|
| Ausgabe: | Second edition |
| Schriftenreihe: | Lecture notes in mathematics
7 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | VII, 176 Seiten |
| ISBN: | 3540045996 0387045996 |
Internformat
MARC
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| 100 | 1 | |a Tondeur, Philippe Maurice |d 1932- |0 (DE-588)125630751 |4 aut | |
| 245 | 1 | 0 | |a Introduction to Lie groups and transformation groups |c Philippe Tondeur |
| 250 | |a Second edition | ||
| 264 | 1 | |a Berlin, [u.a.] |b Springer |c 1969 | |
| 300 | |a VII, 176 Seiten | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 1 | |a Lecture notes in mathematics |v 7 | |
| 650 | 4 | |a Lie groups | |
| 650 | 4 | |a Transformation groups | |
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Datensatz im Suchindex
| _version_ | 1811992274875187200 |
|---|---|
| adam_text |
CONTENTS
1. G Objects
1.1. Definition and examples 1
1.2. Equivariant morphisms 7
1.3. Orbits 13
*1.4. Particular G sets 23
2. G Spaces
2.1. Definition and examples 28
2.2. Orbitspace 30
3. G Manifolds
3.1. Definition and examples of Lie grouos 34
3.2. Definition and examples of G manifolds. . . 37
4. Vectorfields
4.1. Real functions 40
4.2. Operators and vectorfields 42
4.3. The Lie algebra of a Lie group 46
4.4. Effect of maps on operators and
vectorfields 50
4.5. The functor L 52
4.6. Applications of the functoriality of L. 59
4.7. The adjoint representation of a Lie
group 64
5. Vectorflelds and 1 parameter groups of transformations.
5.1. 1 parameter groups of transformations 66
5.2. 1 parameter groups of transformations and
equivariant maps 70
5.3. The bracket of two vectorfields 74
5.4. 1 parameter subgroups of a Lie group 77
5.5. Killing vectorf ields 84
*5.6. The homomorphism a: RG — DX for a G manifold. 89
*5.7. Killing vectorf ields and equivariant maps 96
6. The exponential map of a Lie group.
6.1. Definition and naturality of exp 103
6.2. exp is a local diffeomorphism at the identity. 108
6.3. Unicity of Lie group structure 112
*6.4. Application to fixed points on G manifolds 116
6.5. Taylor's formula 120
7. Subgroups and subalgebras.
7.1. Lie subgroups 128
7.2. Existence of local homomorphisms 132
7.3. Discrete subgroups 138
7.4. Open subgroups; connectedness 142
7.5. Closed subgroups 144
7.6. Closed subgroups of the full linear group 150
7.7. Coset spaces and factor groups 15^
8. Groups of automorphisms.
8.1. The automorphism group of an algeb ra 160
8.2. The adjoint representation of a Lie algebra 162
8.3. The automorphism group of a Lie group 167
Appendix: Categories and functors 170
Bibliography 175 |
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| author | Tondeur, Philippe Maurice 1932- |
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| dewey-full | 512/.86 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
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| dewey-search | 512/.86 |
| dewey-sort | 3512 286 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | Second edition |
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| id | DE-604.BV004548669 |
| illustrated | Not Illustrated |
| indexdate | 2024-10-04T14:01:33Z |
| institution | BVB |
| isbn | 3540045996 0387045996 |
| language | English |
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| physical | VII, 176 Seiten |
| publishDate | 1969 |
| publishDateSearch | 1969 |
| publishDateSort | 1969 |
| publisher | Springer |
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| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Tondeur, Philippe Maurice 1932- (DE-588)125630751 aut Introduction to Lie groups and transformation groups Philippe Tondeur Second edition Berlin, [u.a.] Springer 1969 VII, 176 Seiten txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 7 Lie groups Transformation groups Lie-Gruppe (DE-588)4035695-4 gnd rswk-swf Transformationsgruppe (DE-588)4127386-2 gnd rswk-swf 1\p (DE-588)4151278-9 Einführung gnd-content Transformationsgruppe (DE-588)4127386-2 s DE-604 Lie-Gruppe (DE-588)4035695-4 s Lecture notes in mathematics 7 (DE-604)BV000676446 7 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002798908&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 | Tondeur, Philippe Maurice 1932- Introduction to Lie groups and transformation groups Lecture notes in mathematics Lie groups Transformation groups Lie-Gruppe (DE-588)4035695-4 gnd Transformationsgruppe (DE-588)4127386-2 gnd |
| subject_GND | (DE-588)4035695-4 (DE-588)4127386-2 (DE-588)4151278-9 |
| title | Introduction to Lie groups and transformation groups |
| title_auth | Introduction to Lie groups and transformation groups |
| title_exact_search | Introduction to Lie groups and transformation groups |
| title_full | Introduction to Lie groups and transformation groups Philippe Tondeur |
| title_fullStr | Introduction to Lie groups and transformation groups Philippe Tondeur |
| title_full_unstemmed | Introduction to Lie groups and transformation groups Philippe Tondeur |
| title_short | Introduction to Lie groups and transformation groups |
| title_sort | introduction to lie groups and transformation groups |
| topic | Lie groups Transformation groups Lie-Gruppe (DE-588)4035695-4 gnd Transformationsgruppe (DE-588)4127386-2 gnd |
| topic_facet | Lie groups Transformation groups Lie-Gruppe Transformationsgruppe Einführung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002798908&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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