Classification theory of semi-simple algebraic groups:
Saved in:
| Main Author: | |
|---|---|
| Other Authors: | |
| Format: | Book |
| Language: | English |
| Published: |
New York, [New York]
Marcel Dekker
1971
|
| Series: | Lecture notes in pure and applied mathematics
3 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Enth. ausserdem: Appendix / Mitsuo Sugiura |
| Physical Description: | viii, 149 Seiten |
| ISBN: | 0824716078 |
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| 245 | 1 | 0 | |a Classification theory of semi-simple algebraic groups |c I. Satake ; with an appendix by M. Sugiura |
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| 500 | |a Enth. ausserdem: Appendix / Mitsuo Sugiura | ||
| 650 | 4 | |a Groupes linéaires algébriques | |
| 650 | 4 | |a Linear algebraic groups | |
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Record in the Search Index
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Table of Contents
I. PRELIMINARIES ON ALGEBRAIC GROUPS 1
§1. Affine algebraic sets 1
1.1 Definitions 1
1.2 Rational mappings 4
§2. Affine algebraic groups 6
2.1 Definitions 6
2.2 Rational homomorphisms and quotient groups 9
2.3 Linear algebraic groups 12
2.4 Tori 14
83. K/k forms 18
3.1 K/k forms and one cocycles 18
3.2 Examples of K/k forms 22
3.3 Proof of Prop. 3.1.1 26
84. The structure of algebraic groups 30
4.1 Semi simple and unipotent elements 30
4.2 Solvable groups 31
4.3 Borel subgroups 33
4.4 Questions of rationality 36
II. GENERAL PRINCIPLES OF CLASSIFICATION 43
§1. Structure of semi simple algebraic groups 43
1.1 The root system and the Weyl group 43
1.2 Fundamental systems and Weyl chambers 46
1.3 The fundamental theorem of Chevalley 51
1.4 Some consequences of the fundamental theorem of
Chevalley 57
§2. Structure of semi simple algebraic groups defined over k
(k perfect) 65
2.1 Restricted roots 65
2.2 Structure of parabolic subgroups 73
2.3 The set V is a root system in a wider sense 80
2.4 The fundamental theorem of classification 84
vii
vi i i
§3. Classification of semi simple algebraic groups defined
over k (k perfect) 98
3.1 Investigation of T diagrams 98
3.2 Some special cases (finite fields) 104
3.3 The invariant Y(G) and the classification over
"f adic fields 110
3.U Classification over the real field 123
3.5 Open questions (algebraic number fields) 126
Bibliography 127
Appendix: Classification over the real field, by Mitsuo Sugiura . . 128
Foot notes l44
List of notation 147
Index of terms 148 |
| any_adam_object | 1 |
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| author2 | Sugiura, Mitsuo 1928-2008 |
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| id | DE-604.BV002750974 |
| illustrated | Not Illustrated |
| indexdate | 2025-03-17T11:02:43Z |
| institution | BVB |
| isbn | 0824716078 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001758788 |
| oclc_num | 204500 |
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| physical | viii, 149 Seiten |
| psigel | TUB-nveb |
| publishDate | 1971 |
| publishDateSearch | 1971 |
| publishDateSort | 1971 |
| publisher | Marcel Dekker |
| record_format | marc |
| series | Lecture notes in pure and applied mathematics |
| series2 | Lecture notes in pure and applied mathematics |
| spelling | Satake, Ichiro 1927-2014 (DE-588)172353769 aut Classification theory of semi-simple algebraic groups I. Satake ; with an appendix by M. Sugiura New York, [New York] Marcel Dekker 1971 viii, 149 Seiten txt rdacontent n rdamedia nc rdacarrier Lecture notes in pure and applied mathematics 3 Enth. ausserdem: Appendix / Mitsuo Sugiura Groupes linéaires algébriques Linear algebraic groups Klassifikationstheorie (DE-588)4164034-2 gnd rswk-swf Klassifikation (DE-588)4030958-7 gnd rswk-swf Algebraische Gruppe (DE-588)4001164-1 gnd rswk-swf Algebraische Gruppe (DE-588)4001164-1 s Klassifikation (DE-588)4030958-7 s DE-604 Klassifikationstheorie (DE-588)4164034-2 s Sugiura, Mitsuo 1928-2008 (DE-588)1055751017 ctb Lecture notes in pure and applied mathematics 3 (DE-604)BV005871364 3 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001758788&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Satake, Ichiro 1927-2014 Classification theory of semi-simple algebraic groups Lecture notes in pure and applied mathematics Groupes linéaires algébriques Linear algebraic groups Klassifikationstheorie (DE-588)4164034-2 gnd Klassifikation (DE-588)4030958-7 gnd Algebraische Gruppe (DE-588)4001164-1 gnd |
| subject_GND | (DE-588)4164034-2 (DE-588)4030958-7 (DE-588)4001164-1 |
| title | Classification theory of semi-simple algebraic groups |
| title_auth | Classification theory of semi-simple algebraic groups |
| title_exact_search | Classification theory of semi-simple algebraic groups |
| title_full | Classification theory of semi-simple algebraic groups I. Satake ; with an appendix by M. Sugiura |
| title_fullStr | Classification theory of semi-simple algebraic groups I. Satake ; with an appendix by M. Sugiura |
| title_full_unstemmed | Classification theory of semi-simple algebraic groups I. Satake ; with an appendix by M. Sugiura |
| title_short | Classification theory of semi-simple algebraic groups |
| title_sort | classification theory of semi simple algebraic groups |
| topic | Groupes linéaires algébriques Linear algebraic groups Klassifikationstheorie (DE-588)4164034-2 gnd Klassifikation (DE-588)4030958-7 gnd Algebraische Gruppe (DE-588)4001164-1 gnd |
| topic_facet | Groupes linéaires algébriques Linear algebraic groups Klassifikationstheorie Klassifikation Algebraische Gruppe |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001758788&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV005871364 |
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