Symplectic lie groups:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | French English |
| Veröffentlicht: |
Paris
Société Mathématique de France
2016
|
| Schriftenreihe: | Astérisque
379 |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | vi, 90 Seiten |
| ISBN: | 9782856298343 |
Internformat
MARC
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Datensatz im Suchindex
| _version_ | 1804176321247444992 |
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| adam_text | Titel: Symplectic lie groups
Autor: Baues, Oliver
Jahr: 2016
ASTÉRISQUE 379 SYMPLECTIC LIE GROUPS S O./Baues V. Cortés Société Mathématique de France 2016 Publié avec le concours du Centre National de la Recherche Scientifique
CONTENTS 0. Introduction ............................................................... 1 0.1. Complete reduction of symplectic Lie groups ............................ 3 0.2. Cotangent Lie groups and Lagrangian extensions ........................ 5 0.3. Existence of Lagrangian normal subgroups .............................. 7 0.4. Notation and conventions ............................................... 10 Part I. Theory of reduction ............................................... 15 1. Basic concepts ............................................................. 17 1.1. Isotropic ideals and symplectic rank ..................................... 17 1.2. Symplectic reduction .................................................... 17 1.3. Normal symplectic reduction ............................................ 18 1.4. Symplectic oxidation .................................................... 23 1.5. Lifting and projection of isotropic subalgebras and ideals ............... 26 2. Complete reduction of symplectic Lie algebras ....................... 29 2.1. Complete reduction sequences ........................................... 30 2.2. Completely reducible symplectic Lie algebras ............................ 32 2.3. Symplectic length ....................................................... 35 2.4. Lagrangian subalgebras in irreducible symplectic Lie algebras ........... 36 Part II. Symplectic Lie groups of cotangent type ...................... 43 3. Symplectic geometry of cotangent Lie groups ......................... 45 3.1. Cotangent Lie groups ................................................... 45 3.2. Lagrangian subgroups and induced flat connection ...................... 50 4. Lagrangian extensions of flat Lie algebras ............................. 53 4.1. Lagrangian extensions and strongly polarized symplectic Lie algebras ... 53 4.2. Extension triples associated to Lagrangian reduction .................... 55 4.3.
Functoriality of the correspondence ..................................... 56
CONTENTS vi 4.4. Equivalence classes of Lagrangian extensions ............................ 58 4.5. Lagrangian extension cohomology ....................................... GO Part III. Existence of Lagrangian normal subgroups ................... G3 5. Existence of Lagrangian ideals: basic counterexamples .............. 65 5.1. Solvable symplectic Lie algebras without Lagrangian ideal .............. 65 5.2. Nilpotent Lie algebra of symplectic rank three .......................... 67 6. Endomorphism algebras on symplectic vector spaces ................ 71 6.1. Invariant Lagrangian subspaces for nilpotent endomorphisms ........... 72 6.2. Symplectic quadratic algebras of endomorphisms ........................ 73 6.3. Application to symplectic Lie algebras .................................. 76 7. Isotropic ideals in nilpotent symplectic Lie algebras ................. 77 7.1. Existence of isotropic ideals ............................................. 77 7.2. Filiform symplectic Lie algebras ......................................... 79 8. Three-step nilpotent symplectic Lie algebras .......................... 81 8.1. Lie algebra without Lagrangian ideal .................................... 81 8.2. Three step nilpotent Lie algebras of dimension less than ten ............ 84 Bibliography .................................................................. 87 ASTÉRISQUE 379
|
| any_adam_object | 1 |
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| id | DE-604.BV043587113 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:30:19Z |
| institution | BVB |
| isbn | 9782856298343 |
| language | French English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029001633 |
| oclc_num | 951237661 |
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| physical | vi, 90 Seiten |
| publishDate | 2016 |
| publishDateSearch | 2016 |
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| publisher | Société Mathématique de France |
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| series | Astérisque |
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| spelling | Baues, O. Verfasser (DE-588)1236150864 aut Symplectic lie groups O. Baues, V. Cortés Paris Société Mathématique de France 2016 vi, 90 Seiten txt rdacontent n rdamedia nc rdacarrier Astérisque 379 Cortés, Vicente Verfasser (DE-588)1026703700 aut Astérisque 379 (DE-604)BV002579439 379 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029001633&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Baues, O. Cortés, Vicente Symplectic lie groups Astérisque |
| title | Symplectic lie groups |
| title_auth | Symplectic lie groups |
| title_exact_search | Symplectic lie groups |
| title_full | Symplectic lie groups O. Baues, V. Cortés |
| title_fullStr | Symplectic lie groups O. Baues, V. Cortés |
| title_full_unstemmed | Symplectic lie groups O. Baues, V. Cortés |
| title_short | Symplectic lie groups |
| title_sort | symplectic lie groups |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029001633&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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