Semisimple lie algebras and their classification over p-adic fields:
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| Main Author: | |
|---|---|
| Format: | Thesis Book |
| Language: | English |
| Published: |
2014
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 131 S. graph. Darst. |
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Record in the Search Index
| _version_ | 1804152512631013376 |
|---|---|
| adam_text | CONTENTS
INTRODUCTION 3
1 PREREQUISITES 7
1.1 LIE ALGEBRAS AND ROOT SYSTEMS 7
1.2 P-ADIC FIELDS, CI FIELDS, QUATERNION ALGEBRAS 13
1.3 QUADRATIC, SYMPLECTIC AND HERMITIAN FORMS 14
2 STRUCTURE THEORY AND THE ISOMORPHISM THEOREM 17
2.1 DEFINITION OF THE INVARIANTS 17
2.1.1 TORAL SUBALGEBRAS AND RATIONAL ROOT DECOMPOSITIONS 17
2.1.2 GALOIS ACTIONS AND THE ANISOTROPIC KERNEL 27
2.1.3 RELATIVE WEYL GROUPS, T-LINEAR ORDERS AND THE TWISTED GALOIS
ACTION 34
2.1.4 THE INVARIANTS AND THEIR INDEPENDENCE FROM CHOICES 42
2.2 SPECIAL CASES AND EXAMPLES 46
2.2.1 THE ANISOTROPIC CASE 46
2.2.2 THE QUASI-SPLIT CASE 49
2.2.3 THE SPLIT CASE 54
2.3 THE ISOMORPHISM THEOREM 54
2.3.1 REQUISITES 55
2.3.2 CONSTRUCTION OF THE ISOMORPHISM 58
2.4 VISUALISATION: SATAKE-TITS DIAGRAMS 62
2.4.1 APPLICATION: HOW TO COMPUTE THE RATIONAL ROOT SYSTEM 63
3 CLASSIFICATION OVER GENERAL FIELDS 65
3.1 REDUCTION TO ABSOLUTELY SIMPLE LIE ALGEBRAS 65
3.2 GALOIS COHOMOLOGY AND FORMS OF CERTAIN TYPES 68
3.2.1 APPLICATION: AN EXISTENCE STATEMENT 70
3.3 NECESSARY AND SUFFICIENT CONDITIONS ON THE INDEX 72
3.3.1 THE OPPOSITION INVOLUTION 72
3.3.2 ADMISSIBLE SUBINDICES 73
3.3.3 THE CASE OF FC-RANK 1 75
3.3.4 AN A
N
APPLICATION 76
1
HTTP://D-NB.INFO/1056983566
3.4 SKEW FIELDS AND ANISOTROPIC TYPES 77
3.5 INVOLUTORIAL ALGEBRAS AND THE CLASSICAL TYPES 79
3.5.1 THE FIRST KIND: TYPES B, C AND D 80
3.5.2 THE SECOND KIND: TYPE A 90
3.6 QUASI-SPLIT FORMS 96
4 CLASSIFICATION OVER SPECIAL FIELDS 99
4.1 CL FIELDS AND UNRAMIFIED SPLITTING FOR P-ADIC FIELDS 99
4.2 TYPE AI AND KNESER S THEOREM 101
4.3 TYPES ALL, B, C AND D OVER P-ADIC FIELDS 104
4.3.1 TYPE ALL 104
4.3.2 B
N
105
4.3.3 C
N
106
4.3.4 D
N
107
4.4 EXCEPTIONAL LIE ALGEBRAS OVER P-ADIC FIELDS 109
4.4.1 EQ,
INNER FORMS 109
4.4.2 E
7
112
4.4.3 E
8
114
4.4.4 F
A
115
4.4.5 G
2
116
4.4.6 E
6
, OUTER FORMS 117
4.4.7 DI, TRIALITARIAN TYPES 118
4.5 ABOUT ANISOTROPIC FORMS 119
5 CONCLUDING REMARKS 125
5.1 THE FIELD
K =
R 125
5.2 /C-RATIONAL APPROACHES (ALLISON, SELIGMAN) 125
5.3 EXPLICIT CONSTRUCTIONS FOR EXCEPTIONAL TYPES 126
BIBLIOGRAPHY 127
|
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| spelling | Schoeneberg, Torsten 1983- Verfasser (DE-588)1054048878 aut Semisimple lie algebras and their classification over p-adic fields vorgelegt von Torsten Schoeneberg 2014 131 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Münster (Westfalen), Univ., Diss., 2014 p-adischer Zahlkörper (DE-588)4173065-3 gnd rswk-swf Lie-Algebra (DE-588)4130355-6 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Lie-Algebra (DE-588)4130355-6 s p-adischer Zahlkörper (DE-588)4173065-3 s DE-604 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027509912&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Schoeneberg, Torsten 1983- Semisimple lie algebras and their classification over p-adic fields p-adischer Zahlkörper (DE-588)4173065-3 gnd Lie-Algebra (DE-588)4130355-6 gnd |
| subject_GND | (DE-588)4173065-3 (DE-588)4130355-6 (DE-588)4113937-9 |
| title | Semisimple lie algebras and their classification over p-adic fields |
| title_auth | Semisimple lie algebras and their classification over p-adic fields |
| title_exact_search | Semisimple lie algebras and their classification over p-adic fields |
| title_full | Semisimple lie algebras and their classification over p-adic fields vorgelegt von Torsten Schoeneberg |
| title_fullStr | Semisimple lie algebras and their classification over p-adic fields vorgelegt von Torsten Schoeneberg |
| title_full_unstemmed | Semisimple lie algebras and their classification over p-adic fields vorgelegt von Torsten Schoeneberg |
| title_short | Semisimple lie algebras and their classification over p-adic fields |
| title_sort | semisimple lie algebras and their classification over p adic fields |
| topic | p-adischer Zahlkörper (DE-588)4173065-3 gnd Lie-Algebra (DE-588)4130355-6 gnd |
| topic_facet | p-adischer Zahlkörper Lie-Algebra Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027509912&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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