Left invariant affine structures on nilpotent Lie groups:
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Abschlussarbeit Buch |
| Sprache: | English |
| Veröffentlicht: |
1999
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | 83 S. 30 cm |
Internformat
MARC
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| 100 | 1 | |a Burde, Dietrich |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Left invariant affine structures on nilpotent Lie groups |c Dietrich Burde |
| 264 | 1 | |c 1999 | |
| 300 | |a 83 S. |b 30 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 502 | |a Düsseldorf, Univ., Habil.-Schr. | ||
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Datensatz im Suchindex
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|---|---|
| adam_text |
CONTENTS
INTRODUCTION 5
CHAPTER 1. BACKGROUND ON MILNOR'S CONJECTURE 9
1
.
1
. AFFINE MANIFOLDS 9
1.2. EXISTENCE OF AFFINE STRUCTURES 10
1.3. FUNDAMENTAL GROUPS OF AFFINE MANIFOLDS 11
1.4. LEFT-INVARIANT AFFINE STRUCTURES ON LIE GROUPS 12
1.5. AFFINE STRUCTURES AND REPRESENTATION THEORY 15
1.6. AFFINE AND PROJECTIVE NILMANIFOLDS 16
CHAPTER 2. ALGEBRAIC PRELIMINARIES 17
2.1. AFFINE STRUCTURES ON LIE ALGEBRAS 17
2
.
2
. COHOMOLOGY OF LIE ALGEBRAS 18
2.2.1. BETTI NUMBERS 18
2.2.2. FIRST AND SECOND COHOMOLOGY GROUP 20
2.3. DEFORMATIONS OF LIE ALGEBRAS 22
2.4. FILIFORM LIE ALGEBRAS 23
2.4.1. ADAPTED BASES FOR FILIFORM ALGEBRAS 24
2.5. THE VARIETY OF LIE ALGEBRA LAWS 27
CHAPTER 3. CONSTRUCTION OF AFFINE STRUCTURES 31
3.1. CONDITIONS FOR THE EXISTENCE OF AFFINE STRUCTURES 31
3.1.1. SUFFICIENT CONDITIONS FOR AFFINE STRUCTURES 31
3.1.2. NECESSARY CONDITIONS FOR AFFINE STRUCTURES 36
3.2. TWO CLASSES OF FILIFORM LIE ALGEBRAS 36
3.3. AFFINE STRUCTURES INDUCED BY EXTENSIONS 41
3.4. COMPUTATION OF
H
2
(G, K) 43
3.5. AFFINE STRUCTURES FOR
0
G $N(K), N 11 46
3.5.1. NONSINGULAR DERIVATIONS 47
3.5.2. AFFINE STRUCTURES OF ADJOINT TYPE 49
CHAPTER 4. A REFINEMENT OF ADO'S THEOREM 53
4.1. ELEMENTARY PROPERTIES OF
FI 53
4.2. EXPLICIT FORMULAS FOR /Z 54
4.3. A GENERAL BOUND FOR /Z 56
4.4. FAITHFUL MODULES OF DIMENSION N + 1 63
4.4.1. A-MODULES FOR
N = 10 64
4.4.2. A-MODULES FOR
N = 11 67
CHAPTER 5. COUNTEREXAMPLES TO THE MILNOR CONJECTURE 69
3
BIBLIOGRAFISCHE INFORMATIONEN
HTTP://D-NB.INFO/964997924
4
CONTENTS
5.1. AN OPEN PROBLEM 69
5.2. FILIFORM LIE ALGEBRAS OF DIMENSION 10 70
5.3. FILIFORM LIE ALGEBRAS OF DIMENSION 11 74
5.4. FILIFORM LIE ALGEBRAS OF DIMENSION 12 76
CHAPTER 6. DEUTSCHE ZUSAMMENFASSUNG 77
BIBLIOGRAPHY 81 |
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| illustrated | Not Illustrated |
| indexdate | 2024-10-09T18:11:38Z |
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| language | English |
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| spelling | Burde, Dietrich Verfasser aut Left invariant affine structures on nilpotent Lie groups Dietrich Burde 1999 83 S. 30 cm txt rdacontent n rdamedia nc rdacarrier Düsseldorf, Univ., Habil.-Schr. Hochschulschrift gtt Affine algebraische Mannigfaltigkeit (DE-588)4629829-0 gnd rswk-swf Lie-Algebra (DE-588)4130355-6 gnd rswk-swf Nilpotente Lie-Gruppe (DE-588)4475237-4 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Lie-Algebra (DE-588)4130355-6 s Affine algebraische Mannigfaltigkeit (DE-588)4629829-0 s Nilpotente Lie-Gruppe (DE-588)4475237-4 s DE-604 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010046649&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Burde, Dietrich Left invariant affine structures on nilpotent Lie groups Hochschulschrift gtt Affine algebraische Mannigfaltigkeit (DE-588)4629829-0 gnd Lie-Algebra (DE-588)4130355-6 gnd Nilpotente Lie-Gruppe (DE-588)4475237-4 gnd |
| subject_GND | (DE-588)4629829-0 (DE-588)4130355-6 (DE-588)4475237-4 (DE-588)4113937-9 |
| title | Left invariant affine structures on nilpotent Lie groups |
| title_auth | Left invariant affine structures on nilpotent Lie groups |
| title_exact_search | Left invariant affine structures on nilpotent Lie groups |
| title_full | Left invariant affine structures on nilpotent Lie groups Dietrich Burde |
| title_fullStr | Left invariant affine structures on nilpotent Lie groups Dietrich Burde |
| title_full_unstemmed | Left invariant affine structures on nilpotent Lie groups Dietrich Burde |
| title_short | Left invariant affine structures on nilpotent Lie groups |
| title_sort | left invariant affine structures on nilpotent lie groups |
| topic | Hochschulschrift gtt Affine algebraische Mannigfaltigkeit (DE-588)4629829-0 gnd Lie-Algebra (DE-588)4130355-6 gnd Nilpotente Lie-Gruppe (DE-588)4475237-4 gnd |
| topic_facet | Hochschulschrift Affine algebraische Mannigfaltigkeit Lie-Algebra Nilpotente Lie-Gruppe |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010046649&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT burdedietrich leftinvariantaffinestructuresonnilpotentliegroups |