Lectures on the geometry of Poisson manifolds:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Basel u.a.
Birkhäuser
1994
|
| Series: | Progress in mathematics
118 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VI, 205 S. |
| ISBN: | 3764350164 0817650164 |
Staff View
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Record in the Search Index
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| adam_text | IMAGE 1
IZUVAISMAN
LECTURES ON THE GEOMETRY OF POISSON MANIFOLDS
BIRKHAEUSER VERLAG BASEL * BOSTON * BERLIN
IMAGE 2
TABLE OF CONTENTS
A C K N O W L E D G E M E NT VII
0 I N T R O D U C T I ON 1
1 T HE P O I S S ON B I V E C T OR A ND T HE S C H O U T E N - N I J E N
H U IS
B R A C K ET 5
1.1 T HE POISSON BIVECTOR 5
1.2 T HE SCHOUTEN-NIJENHUIS BRACKET 6
1.3 COORDINATE EXPRESSIONS 9
1.4 T HE KOSZUL FORMULA AND APPLICATIONS 12
1.5 MISCCLLANCA 16
2 T HE S Y M P L E C T IC F O L I A T I ON OF A P O I S S ON M A N I F O
LD 19
2.1 GENERAL DISTRIBUTIONS AND FOLIATIONS 19
2.2 INVOLUTIVITY AND INTEGRABILITY 21
2.3 T HE CASE OF POISSON MANIFOLDS 25
3 E X A M P L ES OF P O I S S ON M A N I F O L DS 31
3.1 STRUCTURES ON M*. LIE-POISSON STRUCTURES 31
3.2 DIRAC BRACKETS 36
3.3 FURTHER EXAMPLES 38
4 P O I S S ON C A L C U L US 41
4.1 T HE BRACKET OF 1-FORMS 41
4.2 T HE CONTRAVARIANT EXTERIOR DIFFERENTIATIONS 43
4.3 T HE REGULAER CASC 48
4.4 COFOLIATIONS 54
4.5 CONTRAVARIANT DERIVATIVES ON VECTOR BUNDLES 55
4.6 MORE BRACKETS 57
5 P O I S S ON C O H O M O L O GY 63
5.1 DEFINITION AND GENERAL PROPERTIES 63
5.2 STRAIGHTFORWARD AND INDUCTIVE COMPUTATIONS 67
5.3 T HE SPECTRAL SEQUENCE OF POISSON COHOMOLOGY 72
5.4 POISSON HOMOLOGY 77
IMAGE 3
VI TABLE OF CONTENTS
6 AN I N T R O D U C T I ON TO Q U A N T I Z A T I ON 83
6.1 PREQUANTIZATION 83
6.2 QUANTIZATION 87
6.3 PREQUANTIZATION REPRESENTATIONS 89
6.4 DEFORMATION QUANTIZATION 92
7 P O I S S ON M O R P H I S M S, C O I N D U C ED S T R U C T U R E S,
R E D U C T I ON 97
7.1 PROPERTIES OF POISSON MAPPINGS 97
7.2 REDUCTION OF POISSON STRUCTURES 101
7.3 GROUP ACTIONS AND M O M E N TA 107
7.4 GROUP ACTIONS AND REDUCTION 110
8 S Y M P L E C T IC R E A L I Z A T I O NS OF P O I S S ON M A N I F O
L DS 115
8.1 LOCAL SYMPLECTIC REALIZATIONS 115
8.2 DUAL PAIRS OF POISSON MANIFOLDS 121
8.3 ISOTROPIE REALIZATIONS 123
8.4 ISOTROPIE REALIZATIONS AND NETS 128
9 R E A L I Z A T I O NS OF P O I S S ON M A N I F O L DS BY
S Y M P L E C T IC G R O U P O I DS 135
9.1 REALIZATIONS OF LIE-POISSON STRUCTURES 135
9.2 T HE LIE GROUPOID A ND SYMPLECTIC STRUCTURES OF T*G 137
9.3 GENERAL SYMPLECTIC GROUPOIDS 143
9.4 LIE ALGEBROIDS AND T HE INTEGRABILITY OF POISSON MANIFOLDS 147
9.5 FURTHER INTEGRABILITY RESULTS 153
10 P O I S S O N - L IE G R O U PS 161
10.1 POISSON-LIE AND BIINVARIANT STRUCTURES ON LIE GROUPS 161
10.2 CHARACTCRISTIC PROPERTIES OF POISSON-LIE GROUPS 164
10.3 T HE LIE ALGEBRA OF A POISSON-LIE GROUP 169
10.4 T HE YANG-BAXTCR EQUATIONS 172
10.5 MANIN TRIPLES 178
10.6 ACTIONS AND DRESSING TRANSFORMATIONS 182
R E F E R E N C ES 189
I N D EX 203
|
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| dewey-full | 516.3/62 |
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| dewey-ones | 516 - Geometry |
| dewey-raw | 516.3/62 |
| dewey-search | 516.3/62 |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:36:50Z |
| institution | BVB |
| isbn | 3764350164 0817650164 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006303539 |
| oclc_num | 29843953 |
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| physical | VI, 205 S. |
| publishDate | 1994 |
| publishDateSearch | 1994 |
| publishDateSort | 1994 |
| publisher | Birkhäuser |
| record_format | marc |
| series | Progress in mathematics |
| series2 | Progress in mathematics |
| spelling | Vaisman, Izu Verfasser aut Lectures on the geometry of Poisson manifolds Izu Vaisman Basel u.a. Birkhäuser 1994 VI, 205 S. txt rdacontent n rdamedia nc rdacarrier Progress in mathematics 118 Manifolds gtt Poisson, variétés de ram Poisson manifolds Poisson-Mannigfaltigkeit (DE-588)4231918-3 gnd rswk-swf Poisson-Mannigfaltigkeit (DE-588)4231918-3 s DE-604 Progress in mathematics 118 (DE-604)BV000004120 118 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006303539&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Vaisman, Izu Lectures on the geometry of Poisson manifolds Progress in mathematics Manifolds gtt Poisson, variétés de ram Poisson manifolds Poisson-Mannigfaltigkeit (DE-588)4231918-3 gnd |
| subject_GND | (DE-588)4231918-3 |
| title | Lectures on the geometry of Poisson manifolds |
| title_auth | Lectures on the geometry of Poisson manifolds |
| title_exact_search | Lectures on the geometry of Poisson manifolds |
| title_full | Lectures on the geometry of Poisson manifolds Izu Vaisman |
| title_fullStr | Lectures on the geometry of Poisson manifolds Izu Vaisman |
| title_full_unstemmed | Lectures on the geometry of Poisson manifolds Izu Vaisman |
| title_short | Lectures on the geometry of Poisson manifolds |
| title_sort | lectures on the geometry of poisson manifolds |
| topic | Manifolds gtt Poisson, variétés de ram Poisson manifolds Poisson-Mannigfaltigkeit (DE-588)4231918-3 gnd |
| topic_facet | Manifolds Poisson, variétés de Poisson manifolds Poisson-Mannigfaltigkeit |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006303539&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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