Algebraic groups and differential Galois theory:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, RI
American Math. Soc.
2011
|
| Series: | Graduate studies in mathematics
122 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 225 S. graph. Darst. |
| ISBN: | 9780821853184 |
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Record in the Search Index
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| adam_text | Titel: Algebraic groups and differential Galois theory
Autor: Crespo, Teresa
Jahr: 2011
Contents
Preface xi
Introduction xiü
Part 1. Algebraic Geometry
Chapter 1. Affine and Projective Varieties 3
§1.1. Affine varieties 3
§1.2. Abstract affine varieties 17
§1.3. Projective varieties 19
Exercises 25
Chapter 2. Algebraic Varieties 27
§2.1. Prevarieties 27
§2.2. Varieties 31
Exercises
Part 2. Algebraic Groups
Chapter 3. Basic Notions 55
§3.1. The notion of algebraic group 55
§3.2. Connected algebraic groups 56
§3.3. Subgroups and morphisms
§3.4. Linearization of affine algebraic groups
§3.5. Homogeneous Spaces 65
§3.6. Characters and semi-invariants 66
vii
59
60
viii__________________________________________________ Contents
§3.7. Quotients 67
Exercises 72
Chapter 4. Lie Algebras and Algebraic Groups 75
§4.1. Lie algebras 75
§4.2. The Lie algebra of a linear algebraic group 79
§4.3. Decomposition of algebraic groups 86
§4.4. Solvable algebraic groups 91
§4.5. Correspondence between algebraic groups and Lie algebras 95
§4.6. Subgroups of SL(2, C) 104
Exercises 115
Part 3. Differential Galois Theory
Chapter 5- Picard-Vessiot Extensions 121
§5.1. Derivations 121
§5.2. Differential rings 122
§5.3. Differential extensions 124
§5.4. The ring of differential Operators 125
§5.5. Homogeneous linear differential equations 126
§5.6. The Picard-Vessiot extension 127
Exercises 133
Chapter 6. The Galois Correspondence 141
§6.1. Differential Galois group 141
§6.2. The differential Galois group as a linear algebraic group 145
§6.3. The fundamental theorem of differential Galois theory 151
§6.4. Liouville extensions 158
§6.5. Generalized Liouville extensions 160
Exercises 162
Chapter 7. Differential Equations over C(z) 165
§7.1. Fuchsian differential equations 165
§7.2. Monodromy group 173
§7.3. Kovacic s algorithm 176
Exercises 211
Contents ix
Chapter 8. Suggestions for Further Reading 215
Bibliography 219
Index 223
|
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| indexdate | 2024-07-09T23:59:41Z |
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| isbn | 9780821853184 |
| language | English |
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| spelling | Crespo, Teresa 1955- Verfasser (DE-588)1014894611 aut Algebraic groups and differential Galois theory Teresa Crespo ; Zbigniew Hajto Providence, RI American Math. Soc. 2011 XIV, 225 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Graduate studies in mathematics 122 Differential-Galois-Theorie (DE-588)4723165-8 gnd rswk-swf Algebraische Gruppe (DE-588)4001164-1 gnd rswk-swf Differential-Galois-Theorie (DE-588)4723165-8 s Algebraische Gruppe (DE-588)4001164-1 s DE-604 Hajto, Zbigniew 1955- Verfasser (DE-588)1014894689 aut Erscheint auch als Online-Ausgabe 978-1-4704-1183-1 Graduate studies in mathematics 122 (DE-604)BV009739289 122 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024151170&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Crespo, Teresa 1955- Hajto, Zbigniew 1955- Algebraic groups and differential Galois theory Graduate studies in mathematics Differential-Galois-Theorie (DE-588)4723165-8 gnd Algebraische Gruppe (DE-588)4001164-1 gnd |
| subject_GND | (DE-588)4723165-8 (DE-588)4001164-1 |
| title | Algebraic groups and differential Galois theory |
| title_auth | Algebraic groups and differential Galois theory |
| title_exact_search | Algebraic groups and differential Galois theory |
| title_full | Algebraic groups and differential Galois theory Teresa Crespo ; Zbigniew Hajto |
| title_fullStr | Algebraic groups and differential Galois theory Teresa Crespo ; Zbigniew Hajto |
| title_full_unstemmed | Algebraic groups and differential Galois theory Teresa Crespo ; Zbigniew Hajto |
| title_short | Algebraic groups and differential Galois theory |
| title_sort | algebraic groups and differential galois theory |
| topic | Differential-Galois-Theorie (DE-588)4723165-8 gnd Algebraische Gruppe (DE-588)4001164-1 gnd |
| topic_facet | Differential-Galois-Theorie Algebraische Gruppe |
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