The structure of complex Lie groups:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton [u.a.]
Chapman & Hall/CRC
2002
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| Series: | Chapman & Hall CRC research notes in mathematics series
429 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references (p. 211-213) and index |
| Physical Description: | x, 218 p. ill. : 24 cm |
| ISBN: | 1584882611 |
Staff View
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| 245 | 1 | 0 | |a The structure of complex Lie groups |c Dong Hoon Lee |
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| adam_text | Contents
Preface vii
1 Complex Lie Groups 1
1.1 Analytic Manifolds 1
1.2 Complex Lie Groups 12
1.3 Examples of Complex Lie Groups 24
1.4 The Automorphism Group 35
1.5 Universal Complexification 39
2 Representative Functions of Lie Groups 49
2.1 Basic Definitions 49
2.2 Algebras of Representative Functions 55
2.3 Proper Automorphism Groups 60
2.4 Analytic Representative Functions 64
2.5 Universal Algebraic Hull 68
2.6 Relative Algebras 73
2.7 Unipotent Hull 77
3 Extensions of Representations 81
3.1 Some Examples 81
3.2 Decomposition Theorem 84
3.3 Main Lemma 88
3.4 Extensions of Representations 91
3.5 Unipotent Analytic Groups 94
3.6 Application to Solvable Groups 96
4 The Structure of Complex Lie Groups 99
4.1 Abelian Complex Analytic Groups 99
4.2 Decomposition of the Adjoint Group 104
ix
x CONTENTS
4.3 Semisimple Complex Analytic Groups 112
4.4 Reductive Complex Analytic Groups 116
4.5 Compact Subgroups of Reductive Groups 119
4.6 Representation Radical 125
4.7 Faithfully Representable Groups 129
4.8 Conjugacy of Reductive Subgroups 132
4.9 Unipotent Hull of Complex Lie Groups 134
5 Algebraic Subgroups in Lie Groups 137
5.1 Affine Algebraic Structure in Lie Groups 137
5.2 Extension Lemma 139
5.3 Affine Algebraic Structure on Reductive Groups . . . 142
5.4 The Maximum Algebraic Subgroup 148
5.5 Further Properties of Reductive Groups 154
6 Observability in Complex Lie Groups 157
6.1 Pro affine Groups and Observability 157
6.2 Observability in Algebraic Groups 165
6.3 Extension of Representative Functions 171
6.4 Structure of Observable Subgroups 174
A Elementary Theory of Lie Algebras 183
A.I Preliminaries 183
A.2 Nilpotent and Solvable Lie Algebras 185
A.3 Semisimple Lie Algebras 188
A.4 Cartan Subalgebras 192
A.5 Campbell Hausdorff Formula 193
B Pro affine Algebraic Groups 197
B.I Hopf Algebras 197
B.2 Pro affine Algebraic Groups 200
Bibliography 211
List of Notations 215
Index 217
|
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| indexdate | 2024-07-09T19:03:07Z |
| institution | BVB |
| isbn | 1584882611 |
| language | English |
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| physical | x, 218 p. ill. : 24 cm |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | Chapman & Hall/CRC |
| record_format | marc |
| series | Chapman & Hall CRC research notes in mathematics series |
| series2 | Chapman & Hall CRC research notes in mathematics series |
| spelling | Lee, Dong-Hoon Verfasser aut The structure of complex Lie groups Dong Hoon Lee Boca Raton [u.a.] Chapman & Hall/CRC 2002 x, 218 p. ill. : 24 cm txt rdacontent n rdamedia nc rdacarrier Chapman & Hall CRC research notes in mathematics series 429 Includes bibliographical references (p. 211-213) and index Grupos de lie larpcal Lie, Groupes de Lie groups Lie-Gruppe (DE-588)4035695-4 gnd rswk-swf Lie-Gruppe (DE-588)4035695-4 s DE-604 Chapman & Hall CRC research notes in mathematics series 429 (DE-604)BV012456897 429 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009882986&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lee, Dong-Hoon The structure of complex Lie groups Chapman & Hall CRC research notes in mathematics series Grupos de lie larpcal Lie, Groupes de Lie groups Lie-Gruppe (DE-588)4035695-4 gnd |
| subject_GND | (DE-588)4035695-4 |
| title | The structure of complex Lie groups |
| title_auth | The structure of complex Lie groups |
| title_exact_search | The structure of complex Lie groups |
| title_full | The structure of complex Lie groups Dong Hoon Lee |
| title_fullStr | The structure of complex Lie groups Dong Hoon Lee |
| title_full_unstemmed | The structure of complex Lie groups Dong Hoon Lee |
| title_short | The structure of complex Lie groups |
| title_sort | the structure of complex lie groups |
| topic | Grupos de lie larpcal Lie, Groupes de Lie groups Lie-Gruppe (DE-588)4035695-4 gnd |
| topic_facet | Grupos de lie Lie, Groupes de Lie groups Lie-Gruppe |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009882986&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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