An introduction to Lie groups and the geometry of homogeneous spaces
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| Format: | Buch |
| Sprache: | English Greek |
| Veröffentlicht: |
Providence, Rhode Island
American Mathematical Society
[2003]
|
| Schriftenreihe: | Student mathematical library
Volume 22 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
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| 100 | 1 | |a Arvanitoyeorgos, Andreas |d 1963- |e Verfasser |0 (DE-588)142306975 |4 aut | |
| 240 | 1 | 0 | |a Homades Lie, homogeneis choroi kai diaphorike geometria |
| 245 | 1 | 0 | |a An introduction to Lie groups and the geometry of homogeneous spaces |c Andreas Arvanitoyeorgos. Translated from the Greek and revised by the author |
| 264 | 1 | |a Providence, Rhode Island |b American Mathematical Society |c [2003] | |
| 264 | 4 | |c © 2003 | |
| 300 | |a xvi, 141 Seiten | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Student mathematical library |v Volume 22 | |
| 650 | 4 | |a Espaces homogènes | |
| 650 | 7 | |a Espaços homogêneos |2 larpcal | |
| 650 | 7 | |a Geometria diferencial |2 larpcal | |
| 650 | 7 | |a Grupos de lie |2 larpcal | |
| 650 | 4 | |a Lie, Groupes de | |
| 650 | 4 | |a Homogeneous spaces | |
| 650 | 4 | |a Lie groups | |
| 650 | 0 | 7 | |a Lie-Gruppe |0 (DE-588)4035695-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Homogener Raum |0 (DE-588)4025787-3 |2 gnd |9 rswk-swf |
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| 830 | 0 | |a Student mathematical library |v Volume 22 |w (DE-604)BV013184751 |9 22 | |
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| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-013165959 | |
Datensatz im Suchindex
| DE-BY-TUM_call_number | 0002 MAT 225f 2010 A 661 0202 MAT 225f 2009 A 496 |
|---|---|
| DE-BY-TUM_katkey | 1656772 |
| DE-BY-TUM_location | 00 02 |
| DE-BY-TUM_media_number | 040006977306 040008163226 040020778850 |
| _version_ | 1820858218900881408 |
| adam_text | Contents
Preface ix
Introduction xi
Chapter 1. Lie Groups 1
1. An example of a Lie group 1
2. Smooth manifolds: A review 2
3. Lie groups 8
4. The tangent space of a Lie group Lie algebras 12
5. One parameter subgroups 15
6. The Campbell Baker Hausdorff formula 20
7. Lie s theorems 21
Chapter 2. Maximal Tori and the Classification Theorem 23
1. Representation theory: elementary concepts 24
2. The adjoint representation 28
3. The Killing form 32
4. Maximal tori 36
5. The classification of compact and connected Lie
groups 39
v
vi Contents
6. Complex semisimple Lie algebras 41
Chapter 3. The Geometry of a Compact Lie Group 51
1. Riemannian manifolds: A review 51
2. Left invariant and bi invariant metrics 59
3. Geometrical aspects of a compact Lie group 61
Chapter 4. Homogeneous Spaces 65
1. Coset manifolds 65
2. Reductive homogeneous spaces 71
3. The isotropy representation 72
Chapter 5. The Geometry of a Reductive Homogeneous Space 77
1. G invariant metrics 77
2. The Riemannian connection 79
3. Curvature 80
Chapter 6. Symmetric Spaces 87
1. Introduction 87
2. The structure of a symmetric space 88
3. The geometry of a symmetric space 91
4. Duality 92
Chapter 7. Generalized Flag Manifolds 95
1. Introduction 95
2. Generalized flag manifolds as adjoint orbits 96
3. Lie theoretic description of a generalized flag mani¬
fold 98
4. Painted Dynkin diagrams 98
5. T roots and the isotropy representation 100
6. G invariant Riemannian metrics 103
7. G invariant complex structures and Kahler metrics 105
Contents vii
8. G invariant Kahler Einstein metrics 108
9. Generalized flag manifolds as complex manifolds 111
Chapter 8. Advanced topics 113
1. Einstein metrics on homogeneous spaces 113
2. Homogeneous spaces in symplectic geometry 118
3. Homogeneous geodesies in homogeneous spaces 123
Bibliography 129
Index 139
|
| any_adam_object | 1 |
| author | Arvanitoyeorgos, Andreas 1963- |
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| author_facet | Arvanitoyeorgos, Andreas 1963- |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.55 |
| dewey-search | 512/.55 |
| dewey-sort | 3512 255 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV019841064 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-23T18:17:11Z |
| institution | BVB |
| isbn | 0821827782 9780821827789 |
| language | English Greek |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-013165959 |
| oclc_num | 52980839 |
| open_access_boolean | |
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| physical | xvi, 141 Seiten |
| publishDate | 2003 |
| publishDateSearch | 2003 |
| publishDateSort | 2003 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | Student mathematical library |
| series2 | Student mathematical library |
| spellingShingle | Arvanitoyeorgos, Andreas 1963- An introduction to Lie groups and the geometry of homogeneous spaces Student mathematical library Espaces homogènes Espaços homogêneos larpcal Geometria diferencial larpcal Grupos de lie larpcal Lie, Groupes de Homogeneous spaces Lie groups Lie-Gruppe (DE-588)4035695-4 gnd Homogener Raum (DE-588)4025787-3 gnd |
| subject_GND | (DE-588)4035695-4 (DE-588)4025787-3 |
| title | An introduction to Lie groups and the geometry of homogeneous spaces |
| title_alt | Homades Lie, homogeneis choroi kai diaphorike geometria |
| title_auth | An introduction to Lie groups and the geometry of homogeneous spaces |
| title_exact_search | An introduction to Lie groups and the geometry of homogeneous spaces |
| title_full | An introduction to Lie groups and the geometry of homogeneous spaces Andreas Arvanitoyeorgos. Translated from the Greek and revised by the author |
| title_fullStr | An introduction to Lie groups and the geometry of homogeneous spaces Andreas Arvanitoyeorgos. Translated from the Greek and revised by the author |
| title_full_unstemmed | An introduction to Lie groups and the geometry of homogeneous spaces Andreas Arvanitoyeorgos. Translated from the Greek and revised by the author |
| title_short | An introduction to Lie groups and the geometry of homogeneous spaces |
| title_sort | an introduction to lie groups and the geometry of homogeneous spaces |
| topic | Espaces homogènes Espaços homogêneos larpcal Geometria diferencial larpcal Grupos de lie larpcal Lie, Groupes de Homogeneous spaces Lie groups Lie-Gruppe (DE-588)4035695-4 gnd Homogener Raum (DE-588)4025787-3 gnd |
| topic_facet | Espaces homogènes Espaços homogêneos Geometria diferencial Grupos de lie Lie, Groupes de Homogeneous spaces Lie groups Lie-Gruppe Homogener Raum |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013165959&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV013184751 |
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