Classification and structure theory of Lie algebras of smooth sections: = Klassifikation und Strukturtheorie von Lie-Algebra glatter Schnitte
Gespeichert in:
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| Format: | Abschlussarbeit Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin
Logos-Verl.
2011
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| Schlagworte: | |
| Online-Zugang: | Inhaltstext Inhaltsverzeichnis |
| Beschreibung: | X, 163 S. 21 cm |
| ISBN: | 9783832530242 383253024X |
Internformat
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| 246 | 1 | 1 | |a Klassifikation und Strukturtheorie von Lie-Algebra glatter Schnitte |
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Datensatz im Suchindex
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IMAGE 1
CONTENTS
1. INTRODUCTION 1
1.1. A SHORT HISTORY OF FINITE-DIMENSIONAL LIE THEORY 1
1.2. INFINITE-DIMENSIONAL LIE ALGEBRAS 2
1.3. REQUIREMENTS AND NOTATION 3
1.4. OUTLINE OF THIS DISSERTATION 4
2. BASIC NOTIONS AND FIRST RESULTS 9
2.1. GENERALITIES ON LIE ALGEBRAS 9
2.2. BUNDLES 22
2.3. LIE ALGEBRA BUNDLES AND LIE ALGEBRAS OF SECTIONS 29
2.3.1. CENTER AND COMMUTATOR 34
2.3.2. DERIVATIONS 35
2.3.3. CENTROID 44
2.3.4. DECOMPOSITIONS 48
2.3.5. COMPLEX STRUCTURES 51
2.3.6. ISOMORPHISMS 52
3. CLASSIFICATION BY HOMOTOPY THEORY 63
3.1. CLASSIFICATION OF BUNDLES OF LIE ALGEBRAS BY HOMOTOPY GROUPS 63
3.2. THE COMPONENT GROUP OF THE AUTOMORPHISM GROUP OF A SIMPLE LIE
ALGEBRA . . 65 3.3. CLASSIFICATION FOR TWO-DIMENSIONAL CLOSED BASE
MANIFOLDS 90
4. UNIVERSAL INVARIANT SYMMETRIC BILINEAR FORMS 95
4.1. UNIVERSAL INVARIANT SYMMETRIC BILINEAR FORMS 95
4.2. COMMUTATIVE PSEUDO-UNITAL ALGEBRAS 100
4.3. UNIVERSAL ISBFS ON TENSOR PRODUCT LIE ALGEBRAS 104
4.4. UNIVERSAL ISBFS ON LIE ALGEBRAS OF SMOOTH SECTIONS 106
4.5. CONTINUOUS UNIVERSAL INVARIANT SYMMETRIC BILINEAR FORMS 109
4.6. CONTINUOUS UNIVERSAL ISBFS ON LIE ALGEBRAS OF SMOOTH SECTIONS 110
5. UNIVERSAL CENTRAL EXTENSIONS 113
5.1. SECOND COHOMOLOGY OF TENSOR PRODUCT LIE ALGEBRAS 113
5.2. UNIVERSAL DIFFERENTIAL MODULES AND 1-FORMS 119
5.3. UNIVERSAL CENTRAL EXTENSIONS OF LIE ALGEBRAS OF SMOOTH SECTIONS 121
6. SECTION ALGEBRAS AS KAC-MOODY ALGEBRAS 125
6.1. THE LOOP REALIZATION OF AFFINE KAC-MOODY ALGEBRAS 125
6.2. APPLYING RESULTS TO GENERALIZED KAC-MOODY ALGEBRAS 127
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/1018408657
DIGITALISIERT DURCH
IMAGE 2
CONTENTS
A. APPENDIX: MORE ON LIE ALGEBRAS 129
A.I. THE CLASSIFICATION OF SEMISIMPLE LIE ALGEBRAS AND AFFINE KAC-MOODY
ALGEBRAS . 129 A.2. UNIVERSAL CENTRAL EXTENSIONS AND LIE ALGEBRA
COHOMOLOGY 138
B. APPENDIX: NOTIONS OF DIFFERENTIAL TOPOLOGY 145
B.I. THE SMOOTH TOPOLOGY ON SPACES OF SMOOTH MAPPINGS 145
B.2. THE OPEN MAPPING THEOREM FOR STRICT LF-SPACES 148
B.3. NON-ABELIAN CECH COHOMOLOGY 149
BIBLIOGRAPHY 153
INDEX OF NOTATIONS 159
INDEX OF TERMS 161 |
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| author | Gündoğan, Hasan 1981- |
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| dewey-full | 512.482 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.482 |
| dewey-search | 512.482 |
| dewey-sort | 3512.482 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Thesis Book |
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| id | DE-604.BV039853606 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-21T00:22:42Z |
| institution | BVB |
| isbn | 9783832530242 383253024X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-024713293 |
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| owner_facet | DE-83 DE-29 DE-29T |
| physical | X, 163 S. 21 cm |
| publishDate | 2011 |
| publishDateSearch | 2011 |
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| publisher | Logos-Verl. |
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| spelling | Gündoğan, Hasan 1981- Verfasser (DE-588)1018665293 aut Classification and structure theory of Lie algebras of smooth sections = Klassifikation und Strukturtheorie von Lie-Algebra glatter Schnitte von Hasan Gündoğan Klassifikation und Strukturtheorie von Lie-Algebra glatter Schnitte Berlin Logos-Verl. 2011 X, 163 S. 21 cm txt rdacontent n rdamedia nc rdacarrier Zugl.: Erlangen-Nürnberg, Univ., Diss., 2011 Vektorraumbündel (DE-588)4187470-5 gnd rswk-swf Lie-Algebra (DE-588)4130355-6 gnd rswk-swf Homotopietheorie (DE-588)4128142-1 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Lie-Algebra (DE-588)4130355-6 s Vektorraumbündel (DE-588)4187470-5 s Homotopietheorie (DE-588)4128142-1 s DE-604 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3949996&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024713293&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Gündoğan, Hasan 1981- Classification and structure theory of Lie algebras of smooth sections = Klassifikation und Strukturtheorie von Lie-Algebra glatter Schnitte Vektorraumbündel (DE-588)4187470-5 gnd Lie-Algebra (DE-588)4130355-6 gnd Homotopietheorie (DE-588)4128142-1 gnd |
| subject_GND | (DE-588)4187470-5 (DE-588)4130355-6 (DE-588)4128142-1 (DE-588)4113937-9 |
| title | Classification and structure theory of Lie algebras of smooth sections = Klassifikation und Strukturtheorie von Lie-Algebra glatter Schnitte |
| title_alt | Klassifikation und Strukturtheorie von Lie-Algebra glatter Schnitte |
| title_auth | Classification and structure theory of Lie algebras of smooth sections = Klassifikation und Strukturtheorie von Lie-Algebra glatter Schnitte |
| title_exact_search | Classification and structure theory of Lie algebras of smooth sections = Klassifikation und Strukturtheorie von Lie-Algebra glatter Schnitte |
| title_full | Classification and structure theory of Lie algebras of smooth sections = Klassifikation und Strukturtheorie von Lie-Algebra glatter Schnitte von Hasan Gündoğan |
| title_fullStr | Classification and structure theory of Lie algebras of smooth sections = Klassifikation und Strukturtheorie von Lie-Algebra glatter Schnitte von Hasan Gündoğan |
| title_full_unstemmed | Classification and structure theory of Lie algebras of smooth sections = Klassifikation und Strukturtheorie von Lie-Algebra glatter Schnitte von Hasan Gündoğan |
| title_short | Classification and structure theory of Lie algebras of smooth sections |
| title_sort | classification and structure theory of lie algebras of smooth sections klassifikation und strukturtheorie von lie algebra glatter schnitte |
| title_sub | = Klassifikation und Strukturtheorie von Lie-Algebra glatter Schnitte |
| topic | Vektorraumbündel (DE-588)4187470-5 gnd Lie-Algebra (DE-588)4130355-6 gnd Homotopietheorie (DE-588)4128142-1 gnd |
| topic_facet | Vektorraumbündel Lie-Algebra Homotopietheorie Hochschulschrift |
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