Simple singularities and simple algebraic groups:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
1980
|
| Series: | Lecture notes in mathematics
815 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 175 S. graph. Darst. |
| ISBN: | 3540100261 0387100261 9783540100263 |
Staff View
MARC
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| 245 | 1 | 0 | |a Simple singularities and simple algebraic groups |c Peter Slodowy |
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Record in the Search Index
| _version_ | 1804116721841209344 |
|---|---|
| adam_text | Table of Contents
I Deformations with Group Actions
1¦ Regular Group Actions
1.1 Conventions 1
1.2 Actions 1
1.3 Linearization 1
1.4 Equivariant Morphisms 2
1.5 Linearly Reductive Groups 3
2. Deformations
2.1 Deformations 4
2.2 Formal Deformations 5
2.3 Semiuniversal Deformations 6
2.4 The Existence of Semiuniversal Deformations 7
2.5 Equi variant Deformations 9
2.6 Deformations with Fixed Symmetries 13
2.7 Deformations with G -action 14
m
2.8 Deformations of Completions 15
II Coniugacy Classes and Singularities in Semisimple Groups
3. The Quotient of the Adjoint Action
3.1 Reductive Groups IV
3.2 Invariants on G 19
3.3 Jordan Decomposition 20
3.4 Centralizers of Semisimple Elements 21
3.5 Rationally Closed Root Subsystems 22
3.6 Torsion 23
VIII
3.7 Associated Fiber Bundles 24
3.8 Regular Elements in Reductive Groups 27
3.9 The Unipotent Variety 28
3.10 Fibers of the Adjoint Quotient 30
3.11 An Example 33
3.12 Invariants on the Lie algebra 36
3.13 Very Good Primes 37
3.14 The fibers of y 39
3.15 A Comparison Theorem 41
4. The Resolution of the Adjoint Quotient
4.1 The Resolution of the Singularities of the Unipotent Variety 43
4.2 Simultaneous Resolutions 45
4.3 Several Constructions 46
4.4 The Simultaneous Resolution of x 50
4.5 The Situation for Non-Simply Connected Groups 51
4.6 A Generalization 54
4.7 Carrying over to Lie Algebras 58
III Simple Singularities in Simple Groups
5. Subregular Singularities
5.1 Transverse Slices 60
5.2 The Restriction of Invariants to Transverse Slices 64
5.3 Simultaneous Resolutions for Transverse Slices 65
5.4 Subregular Elements 67
5.5 Subregular Singularities 69
6. Simple Singularities
6.1 Rational Double Points 70
IX
6.2 Symmetries on Rational Double Points 75
6.3 Dynkin Curves 85
6.4 The Identification of Subregular Singularities 88
6.5 The Neighboring Singularities 93
6.6 The Neighboring Fibers 96
IV Deformations of Simple Singularities
7. Nilpotent Elements in Simple Lie Algebras
7.1 Representation Theory for the Lie Algebra si 103
7.2 The Jacobson-Morozov Lemma 105
7.3 The Classification of Nilpotent Elements 106
7.4 A Special Transverse Slice 109
7.5 Centralization of Nilpotent Elements 114
7.6 Outer Centralization of Nilpotent Elements 117
8. Deformations of Simple Singularities
8.1 Some Aids 121
8.2 The Subregular Deformations 123
8.3 An Alternative Identification of the Subregular Singularities 124
8.4 The Simplicity of the Subregular Singularities 128
8.5 A Supplement to 7.5 133
8.6 The G -structure of the Semiuniversal Deformations of the Simple
m
Singularities 134
8.7 The Semiuniversality of the Subregular Deformations 136
8.8 Outer Automorphisms and Associated Symmetries 139
8.9 Simultaneous Resolutions 145
8.10 The Neighboring Fibers of Semiuniversal Deformations 146
8.11 other Applications 149
X
Appendix I
Forms of Simple Singularities and Simple Groups 152
Appendix II
A Semiuniversality Property of Adjoint Quotients 160
Appendix III
DynJcin Diagrams and Representations of Finite Subgroups of SL_ 162
Bibliography 167
Subject Index 173
|
| any_adam_object | 1 |
| author | Slodowy, Peter 1948-2002 |
| author_GND | (DE-588)132170736 |
| author_facet | Slodowy, Peter 1948-2002 |
| author_role | aut |
| author_sort | Slodowy, Peter 1948-2002 |
| author_variant | p s ps |
| building | Verbundindex |
| bvnumber | BV002264215 |
| callnumber-first | Q - Science |
| callnumber-label | QA3 |
| callnumber-raw | QA3 |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SI 850 |
| ctrlnum | (OCoLC)6626996 (DE-599)BVBBV002264215 |
| dewey-full | 510 512/.33 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics 512 - Algebra |
| dewey-raw | 510 512/.33 |
| dewey-search | 510 512/.33 |
| dewey-sort | 3510 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| isbn | 3540100261 0387100261 9783540100263 |
| language | English |
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| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Slodowy, Peter 1948-2002 Verfasser (DE-588)132170736 aut Simple singularities and simple algebraic groups Peter Slodowy Berlin [u.a.] Springer 1980 X, 175 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 815 Groupes linéaires algébriques Géométrie algébrique Lie, Algèbres de Singularités (Mathématiques) Geometry, Algebraic Lie algebras Linear algebraic groups Singularities (Mathematics) Einfache Gruppe (DE-588)4123107-7 gnd rswk-swf Einfache algebraische Gruppe (DE-588)4151265-0 gnd rswk-swf Einfache Singularität (DE-588)4151268-6 gnd rswk-swf Auflösung von Singularitäten (DE-588)4181537-3 gnd rswk-swf 1\p (DE-588)4113937-9 Hochschulschrift gnd-content Auflösung von Singularitäten (DE-588)4181537-3 s DE-604 Einfache Gruppe (DE-588)4123107-7 s Einfache Singularität (DE-588)4151268-6 s Einfache algebraische Gruppe (DE-588)4151265-0 s Lecture notes in mathematics 815 (DE-604)BV000676446 815 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001487952&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Slodowy, Peter 1948-2002 Simple singularities and simple algebraic groups Lecture notes in mathematics Groupes linéaires algébriques Géométrie algébrique Lie, Algèbres de Singularités (Mathématiques) Geometry, Algebraic Lie algebras Linear algebraic groups Singularities (Mathematics) Einfache Gruppe (DE-588)4123107-7 gnd Einfache algebraische Gruppe (DE-588)4151265-0 gnd Einfache Singularität (DE-588)4151268-6 gnd Auflösung von Singularitäten (DE-588)4181537-3 gnd |
| subject_GND | (DE-588)4123107-7 (DE-588)4151265-0 (DE-588)4151268-6 (DE-588)4181537-3 (DE-588)4113937-9 |
| title | Simple singularities and simple algebraic groups |
| title_auth | Simple singularities and simple algebraic groups |
| title_exact_search | Simple singularities and simple algebraic groups |
| title_full | Simple singularities and simple algebraic groups Peter Slodowy |
| title_fullStr | Simple singularities and simple algebraic groups Peter Slodowy |
| title_full_unstemmed | Simple singularities and simple algebraic groups Peter Slodowy |
| title_short | Simple singularities and simple algebraic groups |
| title_sort | simple singularities and simple algebraic groups |
| topic | Groupes linéaires algébriques Géométrie algébrique Lie, Algèbres de Singularités (Mathématiques) Geometry, Algebraic Lie algebras Linear algebraic groups Singularities (Mathematics) Einfache Gruppe (DE-588)4123107-7 gnd Einfache algebraische Gruppe (DE-588)4151265-0 gnd Einfache Singularität (DE-588)4151268-6 gnd Auflösung von Singularitäten (DE-588)4181537-3 gnd |
| topic_facet | Groupes linéaires algébriques Géométrie algébrique Lie, Algèbres de Singularités (Mathématiques) Geometry, Algebraic Lie algebras Linear algebraic groups Singularities (Mathematics) Einfache Gruppe Einfache algebraische Gruppe Einfache Singularität Auflösung von Singularitäten Hochschulschrift |
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| work_keys_str_mv | AT slodowypeter simplesingularitiesandsimplealgebraicgroups |