An introduction to Lie groups and the geometry of homogeneous spaces:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English Greek |
| Published: |
Providence, Rhode Island
American Mathematical Society
[2003]
|
| Series: | Student mathematical library
Volume 22 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xvi, 141 Seiten |
| ISBN: | 0821827782 9780821827789 |
Staff View
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV019841064 | ||
| 003 | DE-604 | ||
| 005 | 20230313 | ||
| 007 | t | ||
| 008 | 050610s2003 |||| 00||| eng d | ||
| 020 | |a 0821827782 |9 0-8218-2778-2 | ||
| 020 | |a 9780821827789 |9 978-0-8218-2778-9 | ||
| 035 | |a (OCoLC)52980839 | ||
| 035 | |a (DE-599)BVBBV019841064 | ||
| 040 | |a DE-604 |b ger |e rda | ||
| 041 | 1 | |a eng |h gre | |
| 049 | |a DE-19 |a DE-20 |a DE-91G |a DE-91 |a DE-11 | ||
| 050 | 0 | |a QA387 | |
| 082 | 0 | |a 512/.55 |2 22 | |
| 084 | |a SK 340 |0 (DE-625)143232: |2 rvk | ||
| 084 | |a SK 370 |0 (DE-625)143234: |2 rvk | ||
| 084 | |a MAT 225f |2 stub | ||
| 084 | |a MAT 537f |2 stub | ||
| 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 |
| 689 | 0 | 0 | |a Homogener Raum |0 (DE-588)4025787-3 |D s |
| 689 | 0 | 1 | |a Lie-Gruppe |0 (DE-588)4035695-4 |D s |
| 689 | 0 | |5 DE-604 | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-1-4704-2136-6 |
| 830 | 0 | |a Student mathematical library |v Volume 22 |w (DE-604)BV013184751 |9 22 | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u 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 |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-013165959 | ||
Record in the Search Index
| _version_ | 1804133351881179136 |
|---|---|
| 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- |
| author_GND | (DE-588)142306975 |
| author_facet | Arvanitoyeorgos, Andreas 1963- |
| author_role | aut |
| author_sort | Arvanitoyeorgos, Andreas 1963- |
| author_variant | a a aa |
| building | Verbundindex |
| bvnumber | BV019841064 |
| callnumber-first | Q - Science |
| callnumber-label | QA387 |
| callnumber-raw | QA387 |
| callnumber-search | QA387 |
| callnumber-sort | QA 3387 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 340 SK 370 |
| classification_tum | MAT 225f MAT 537f |
| ctrlnum | (OCoLC)52980839 (DE-599)BVBBV019841064 |
| dewey-full | 512/.55 |
| 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 |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>02204nam a2200553 cb4500</leader><controlfield tag="001">BV019841064</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20230313 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">050610s2003 |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0821827782</subfield><subfield code="9">0-8218-2778-2</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780821827789</subfield><subfield code="9">978-0-8218-2778-9</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)52980839</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV019841064</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rda</subfield></datafield><datafield tag="041" ind1="1" ind2=" "><subfield code="a">eng</subfield><subfield code="h">gre</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-19</subfield><subfield code="a">DE-20</subfield><subfield code="a">DE-91G</subfield><subfield code="a">DE-91</subfield><subfield code="a">DE-11</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA387</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">512/.55</subfield><subfield code="2">22</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 340</subfield><subfield code="0">(DE-625)143232:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 370</subfield><subfield code="0">(DE-625)143234:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 225f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 537f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Arvanitoyeorgos, Andreas</subfield><subfield code="d">1963-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)142306975</subfield><subfield code="4">aut</subfield></datafield><datafield tag="240" ind1="1" ind2="0"><subfield code="a">Homades Lie, homogeneis choroi kai diaphorike geometria</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">An introduction to Lie groups and the geometry of homogeneous spaces</subfield><subfield code="c">Andreas Arvanitoyeorgos. Translated from the Greek and revised by the author</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Providence, Rhode Island</subfield><subfield code="b">American Mathematical Society</subfield><subfield code="c">[2003]</subfield></datafield><datafield tag="264" ind1=" " ind2="4"><subfield code="c">© 2003</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">xvi, 141 Seiten</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Student mathematical library</subfield><subfield code="v">Volume 22</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Espaces homogènes</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Espaços homogêneos</subfield><subfield code="2">larpcal</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Geometria diferencial</subfield><subfield code="2">larpcal</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Grupos de lie</subfield><subfield code="2">larpcal</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Lie, Groupes de</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Homogeneous spaces</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Lie groups</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Lie-Gruppe</subfield><subfield code="0">(DE-588)4035695-4</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Homogener Raum</subfield><subfield code="0">(DE-588)4025787-3</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Homogener Raum</subfield><subfield code="0">(DE-588)4025787-3</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Lie-Gruppe</subfield><subfield code="0">(DE-588)4035695-4</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Online-Ausgabe</subfield><subfield code="z">978-1-4704-2136-6</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Student mathematical library</subfield><subfield code="v">Volume 22</subfield><subfield code="w">(DE-604)BV013184751</subfield><subfield code="9">22</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HBZ Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">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</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-013165959</subfield></datafield></record></collection> |
| id | DE-604.BV019841064 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T20:07:21Z |
| institution | BVB |
| isbn | 0821827782 9780821827789 |
| language | English Greek |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-013165959 |
| oclc_num | 52980839 |
| open_access_boolean | |
| owner | DE-19 DE-BY-UBM DE-20 DE-91G DE-BY-TUM DE-91 DE-BY-TUM DE-11 |
| owner_facet | DE-19 DE-BY-UBM DE-20 DE-91G DE-BY-TUM DE-91 DE-BY-TUM DE-11 |
| 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 |
| spelling | Arvanitoyeorgos, Andreas 1963- Verfasser (DE-588)142306975 aut Homades Lie, homogeneis choroi kai diaphorike geometria An introduction to Lie groups and the geometry of homogeneous spaces Andreas Arvanitoyeorgos. Translated from the Greek and revised by the author Providence, Rhode Island American Mathematical Society [2003] © 2003 xvi, 141 Seiten txt rdacontent n rdamedia nc rdacarrier Student mathematical library Volume 22 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 rswk-swf Homogener Raum (DE-588)4025787-3 gnd rswk-swf Homogener Raum (DE-588)4025787-3 s Lie-Gruppe (DE-588)4035695-4 s DE-604 Erscheint auch als Online-Ausgabe 978-1-4704-2136-6 Student mathematical library Volume 22 (DE-604)BV013184751 22 HBZ Datenaustausch application/pdf 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 Inhaltsverzeichnis |
| 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 |
| work_keys_str_mv | AT arvanitoyeorgosandreas homadesliehomogeneischoroikaidiaphorikegeometria AT arvanitoyeorgosandreas anintroductiontoliegroupsandthegeometryofhomogeneousspaces |