Lie group actions in complex analysis:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Braunschweig u.a.
Vieweg
1995
|
| Series: | [Aspects of mathematics / E]
27 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VII, 201 S. |
| ISBN: | 352806420X |
Staff View
MARC
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| 245 | 1 | 0 | |a Lie group actions in complex analysis |c Dmitri N. Akhiezer |
| 264 | 1 | |a Braunschweig u.a. |b Vieweg |c 1995 | |
| 300 | |a VII, 201 S. | ||
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Record in the Search Index
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| adam_text | vi
Contents
Introduction 1
1 Lie theory 3
1.1 Complex spaces 3
1.2 Lie group actions 6
1.3 One parameter transformation groups 10
1.4 Vector fields 14
1.5 Infinitesimal transformations 16
1.6 Analyticity of Lie group actions 20
1.7 Lie homomorphism 22
1.8 Global actions 27
2 Automorphism groups 31
2.1 Topology in Hol(X, Y) 31
2.2 Local linearization of a compact group with a fixed point 35
2.3 The automorphism group of a compact complex space 39
2.4 Automorphisms of fiber bundles 44
2.5 Proper actions 48
2.6 The automorphism group of a bounded domain 50
2.7 The automorphism groups of the polydisk and the ball 54
2.8 A characterization of the ball 57
2.9 Bounded domains with compact quotient D/Aut(D) 61
3 Compact homogeneous manifolds 63
3.1 Flag manifolds 63
3.2 Equivariant projective embeddings 70
3.3 Automorphism groups of flag manifolds 73
3.4 Parallelizable manifolds 77
3.5 Tits fibration 79
3.6 Manifolds fibered by tori 82
3.7 The role of the fundamental group 85
3.8 An estimate of the dimension of Aut(X) 96
3.9 Compact homogeneous Kahler manifolds 100
Contents vii
4 Homogeneous vector bundles 105
4.1 Coherent analytic G sheaves 105
4.2 Holomorphic vector G bundles 110
4.3 Theorem of R.Bott. Proof of the Borel Weil theorem 113
4.4 Application of the Leray spectral sequence 116
4.5 Proof of the theorem of R.Bott 118
4.6 Invertible sheaves on G/P for P maximal parabolic 121
4.7 Computations in root systems 125
4.8 Cohomology of the tangent sheaf 130
5 Function theory on homogeneous manifolds 135
5.1 Representations of compact Lie groups on Frechet spaces 135
5.2 Differentiable vectors and Fourier series in O(X) 144
5.3 Reductive complex Lie groups 147
5.4 Quasi affine homogeneous varieties 153
5.5 Holomorphically separable homogeneous manifolds 157
5.6 Stein homogeneous manifolds 159
5.7 Observable subgroups 164
5.8 Invariant plurisubharmonic functions and geodesic convexity 171
Concluding remarks 181
Bibliography 186
Index of notations 196
Index of terminology 199
|
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| author_GND | (DE-588)101377048X |
| author_facet | Achiezer, Dmitrij N. 1946- |
| author_role | aut |
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| discipline | Mathematik |
| format | Book |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:44:18Z |
| institution | BVB |
| isbn | 352806420X |
| language | English |
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| physical | VII, 201 S. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| publisher | Vieweg |
| record_format | marc |
| series2 | [Aspects of mathematics / E] |
| spelling | Achiezer, Dmitrij N. 1946- Verfasser (DE-588)101377048X aut Lie group actions in complex analysis Dmitri N. Akhiezer Braunschweig u.a. Vieweg 1995 VII, 201 S. txt rdacontent n rdamedia nc rdacarrier [Aspects of mathematics / E] 27 Lie-Gruppe (DE-588)4035695-4 gnd rswk-swf Gruppenoperation (DE-588)4158467-3 gnd rswk-swf Komplexer Raum (DE-588)4138419-2 gnd rswk-swf Lie-Gruppe (DE-588)4035695-4 s Komplexer Raum (DE-588)4138419-2 s DE-604 Gruppenoperation (DE-588)4158467-3 s E] [Aspects of mathematics 27 (DE-604)BV000018737 27 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006613641&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Achiezer, Dmitrij N. 1946- Lie group actions in complex analysis Lie-Gruppe (DE-588)4035695-4 gnd Gruppenoperation (DE-588)4158467-3 gnd Komplexer Raum (DE-588)4138419-2 gnd |
| subject_GND | (DE-588)4035695-4 (DE-588)4158467-3 (DE-588)4138419-2 |
| title | Lie group actions in complex analysis |
| title_auth | Lie group actions in complex analysis |
| title_exact_search | Lie group actions in complex analysis |
| title_full | Lie group actions in complex analysis Dmitri N. Akhiezer |
| title_fullStr | Lie group actions in complex analysis Dmitri N. Akhiezer |
| title_full_unstemmed | Lie group actions in complex analysis Dmitri N. Akhiezer |
| title_short | Lie group actions in complex analysis |
| title_sort | lie group actions in complex analysis |
| topic | Lie-Gruppe (DE-588)4035695-4 gnd Gruppenoperation (DE-588)4158467-3 gnd Komplexer Raum (DE-588)4138419-2 gnd |
| topic_facet | Lie-Gruppe Gruppenoperation Komplexer Raum |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006613641&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000018737 |
| work_keys_str_mv | AT achiezerdmitrijn liegroupactionsincomplexanalysis |