Infinite dimensional Kähler manifolds:
Gespeichert in:
| Format: | Buch |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
Basel [u.a.]
Birkhäuser
2001
|
| Schriftenreihe: | DMV-Seminar
31 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturangaben |
| Beschreibung: | XIII, 375 S. 24 cm |
| ISBN: | 3764366028 |
Internformat
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| 245 | 1 | 0 | |a Infinite dimensional Kähler manifolds |c Alan Huckleberry ... ed. |
| 264 | 1 | |a Basel [u.a.] |b Birkhäuser |c 2001 | |
| 300 | |a XIII, 375 S. |b 24 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a DMV-Seminar |v 31 | |
| 500 | |a Literaturangaben | ||
| 650 | 7 | |a Globale analyse |2 gtt | |
| 650 | 7 | |a Topologische groepen |2 gtt | |
| 650 | 4 | |a Variétés kählériennes | |
| 650 | 4 | |a Kählerian manifolds | |
| 650 | 0 | 7 | |a Kähler-Mannigfaltigkeit |0 (DE-588)4162978-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Unendlichdimensionale Mannigfaltigkeit |0 (DE-588)4433823-5 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Kähler-Mannigfaltigkeit |0 (DE-588)4162978-4 |D s |
| 689 | 0 | 1 | |a Unendlichdimensionale Mannigfaltigkeit |0 (DE-588)4433823-5 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Huckleberry, Alan |d 1941- |e Sonstige |0 (DE-588)108548996 |4 oth | |
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Datensatz im Suchindex
| _version_ | 1804128653856997376 |
|---|---|
| adam_text | Contents
Préface xi
Introduction to Group Actions in Symplectic and Complex Geometry
Alan Huckleberry
I. Finite-dimensional manifolds 1
1. Vector space structures 1
2. Local theory 4
3. Global differentiable objects 5
4. A sketch of intégration theory 13
5. Smooth submanifolds 15
6. Induced orientation and Stokes theorem 17
7. Functionals on de Rham cohomology 19
II. Elements of Lie groups and their actions 20
1. Introduction to actions and quotients 20
2. Examples of Lie groups 21
3. Smooth actions of Lie groups 26
4. Fiber bundles 35
III. Manifolds with additional structure 40
1. Geometrie structures on vector Spaces 40
2. The éléments of function theory 46
3. A brief introduction to complex analysis in higher dimensions 53
4. Complex manifolds 58
5. Symplectic manifolds 70
6. Kahler manifolds 78
IV. Symplectic manifolds with symmetry 82
1. Introduction to the moment map 82
2. Central extensions 85
3. Existence and uniqueness of the moment map 88
4. Basic examples of the moment map 89
5. The Poisson structure on (Lie G)* and on coadjoint orbits 92
6. The basic formula and some conséquences 94
7. Moment maps associated to représentations 94
vi Contents
V. Kählerian structures on coadjoint orbits of compact groups
and associated représentations 95
1. Generalities on compact groups 95
2. Root décomposition for tc 98
3. Complexification of compact groups 102
4. Algebraicity properties of complexifications of compact groups 105
5. Compact complex homogeneous spaces 107
6. The root groups SL2{a) and H2(G/P, Z) 115
7. Représentations of complex semisimple groups 123
Literature 128
Infinite-dimensional Groups and their Représentations
Karl-Hermann Neeb
Introduction 131
I. Calculus in locally convex spaces 132
1. Differentiable functions 133
2. Differentiable functions on Banach spaces 135
3. Holomorphic functions 138
4. Differentiable manifolds 140
5. Infinite-dimensional Lie groups 142
II. Dual spaces of locally convex spaces 144
1. Metrizability 146
2. Semireflexivity 148
3. Completeness properties of the dual space 150
III. Topologies on function spaces 153
1. The space C°°(M, V) 153
2. Smooth mappings between function spaces 158
3. Applications to groups of continuous mappings 159
4. Spaces of holomorphic functions 160
IV. Représentations of infinite-dimensional groups 164
V. Generalized cohérent state représentations 168
1. The line bündle over the projective space of a
topological vector space 168
2. Applications to représentation theory 172
Références 177
Contents vii
Borel-Weil Theory for Loop Groups
Karl-Hermann Neeb
Introduction 179
I. Compact groups 180
II. Loop groups and their central extensions 181
1. Groups of smooth maps 181
2. Central extensions of loop groups 184
3. Appendix Ha: Central extensions and semidirect producís 185
4. Appendix Ilb: Smoothness of group actions 188
5. Appendix Ile: Lifting automorphisms to central extensions 189
6. Appendix lid: Lifting automorphic group actions
to central extensions 192
III. Root décompositions 197
1. The Weyl group 198
2. Root décomposition of the central extension 200
IV. Représentations of loop groups 201
1. Lowest weight vectors and antidominant weights 203
2. The Casimir Operator 206
V. Representations of involutive semigroups 209
VI. Borel-Weil theory 213
VII. Conséquences for general représentations 226
Références 228
Coadjoint Représentation of Virasoro-type Lie Algebras
and Differential Operators on Tensor-densities
Valentin Yu. Ovsienko
Introduction 231
I. Coadjoint representation of Virasoro group and Sturm-Liouville Operators;
Schwarzian derivative as a 1-cocycle 233
1. Virasoro group and Virasoro algebra 233
2. Regularized dual space 234
3. Coadjoint représentation of the Virasoro algebra 235
4. The coadjoint action of Virasoro group and
Schwarzian derivative 236
5. Space of Sturm-Liouville equations as a Diff+(S 1)-module 236
viii Contents
6. The isomorphism 237
7. Vect(S 1)-action on the space of Sturm-Liouville Operators 238
II. Projectively invariant version of the Gelfand-Fuchs cocycle
and of the Schwarzian derivative 238
1. Modified Gelfand-Fuchs cocycle 239
2. Modified Schwarzian derivative 239
3. Energy shift 240
4. Projective structures 240
III. Kirillov s method of Lie superalgebras 241
1. Lie superalgebras 241
2. Ramond and Neveu-Schwarz superalgebras 242
3. Coadjoint représentation 243
4. Projective equivariance and Lie superalgebra osp(l|2) 243
IV. Invariants of coadjoint représentation of the Virasoro group 244
1. Monodromy Operator as a conjugation class of SL(2, R) 244
2. Classification theorem 245
V. Extension of the Lie algebra of first order linear differential Operators
on S1 and matrix analogue of the Sturm-Liouville Operator 247
1. Lie algebra of first order differential Operators on S1
and its central extensions 247
2. Matrix Sturm-Liouville Operators 247
3. Action of Lie algebra of differential Operators 248
4. Generalized Neveu-Schwarz superalgebra 248
VI. Geometrical définition of the Gelfand-Dickey bracket and
the relation to the Moyal-Weil star-product 249
1. Moyal-Weyl star-product 250
2. Moyal-Weyl star-product on tensor-densities, the transvectants .... 250
3. Space of third order linear differential Operators
as a Diff+CS^-module 251
4. Second order Lie derivative 252
5. Adler-Gelfand-Dickey Poisson structure 253
Références 253
Contents ix
From Group Actions to Déterminant Bundles
Using (Heat-kernel) Renormalization Techniques
Sylvie Paycha
Introduction 257
I. Renormalization techniques 260
1. Renormalized limits 260
2. Renormalization procédures 261
3. Heat-kernel renormalization procédures 262
4. Renormalized déterminants 264
IL The first Chern form on a class of hermitian vector bundles 266
1. Renormalization procédures on vector bundles 266
2. Weighted first Chern forms on infinite
dimensional vector bundles 268
III. The geometry of gauge orbits 270
1. The finite dimensional setting 270
2. The infinite dimensional setting 272
IV. The geometry of déterminant bundles 275
1. Determinant bundles 275
2. A metric on the determinant bündle 276
3. A connection on the determinant bündle 276
4. Curvature on the determinant bündle 277
V. An example: the action of diffeomorphisms on complex structures ... 278
1. The orbit picture 278
2. Riemannian structures 279
3. A super vector bündle arising from the group action 280
4. The déterminant bündle picture 281
5. First Chern form on the vector bündle 282
Références 283
x Contents
Fermionic Second Quantization and the Geometry of
the Restricted Grassmannian
Tilmann Wurzbacher
Introduction 287
I. Fermionic second quantization 290
1. The Dirac équation and the negative energy problem 291
2. Fermionic multiparticle formalism:
Fock space and the CAR-algebra 293
II. Bogoliubov transformations and the Schwinger term 298
1. Implementation of Operators on the Fock space 298
2. The Schwinger term 308
3. The central extensions U~s and GL~S 316
III. The restricted Grassmannian of a polarized Hubert space 326
1. The restricted Grassmannian as a homogeneous
complex manifold 326
2. The basic differential geometry of the
restricted Grassmannian 332
IV. The non-equivariant moment map of the
restricted Grassmannian 336
1. Differential fc-forms in infinite dimensions 336
2. Symplectic manifolds, group actions and the co-moment map 343
3. Co-momentum and momentum maps (in infinite dimensions) 347
4. Examples of symplectic actions and (co-)momementum maps 352
5. The f/res-moment map on GTes and the Schwinger term 354
V. The déterminant Une bündle on the restricted Grassmannian 358
1. The C*-algebraic construction of the determinant bündle DET 358
2. Comparison to other approaches to the determinant bündle 361
3. Holomorphic sections of the dual of DET 366
Références 370
|
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| id | DE-604.BV013824303 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:52:40Z |
| institution | BVB |
| isbn | 3764366028 |
| language | English |
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| physical | XIII, 375 S. 24 cm |
| publishDate | 2001 |
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| series | DMV-Seminar |
| series2 | DMV-Seminar |
| spelling | Infinite dimensional Kähler manifolds Alan Huckleberry ... ed. Basel [u.a.] Birkhäuser 2001 XIII, 375 S. 24 cm txt rdacontent n rdamedia nc rdacarrier DMV-Seminar 31 Literaturangaben Globale analyse gtt Topologische groepen gtt Variétés kählériennes Kählerian manifolds Kähler-Mannigfaltigkeit (DE-588)4162978-4 gnd rswk-swf Unendlichdimensionale Mannigfaltigkeit (DE-588)4433823-5 gnd rswk-swf Kähler-Mannigfaltigkeit (DE-588)4162978-4 s Unendlichdimensionale Mannigfaltigkeit (DE-588)4433823-5 s DE-604 Huckleberry, Alan 1941- Sonstige (DE-588)108548996 oth DMV-Seminar 31 (DE-604)BV000020322 31 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009454375&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Infinite dimensional Kähler manifolds DMV-Seminar Globale analyse gtt Topologische groepen gtt Variétés kählériennes Kählerian manifolds Kähler-Mannigfaltigkeit (DE-588)4162978-4 gnd Unendlichdimensionale Mannigfaltigkeit (DE-588)4433823-5 gnd |
| subject_GND | (DE-588)4162978-4 (DE-588)4433823-5 |
| title | Infinite dimensional Kähler manifolds |
| title_auth | Infinite dimensional Kähler manifolds |
| title_exact_search | Infinite dimensional Kähler manifolds |
| title_full | Infinite dimensional Kähler manifolds Alan Huckleberry ... ed. |
| title_fullStr | Infinite dimensional Kähler manifolds Alan Huckleberry ... ed. |
| title_full_unstemmed | Infinite dimensional Kähler manifolds Alan Huckleberry ... ed. |
| title_short | Infinite dimensional Kähler manifolds |
| title_sort | infinite dimensional kahler manifolds |
| topic | Globale analyse gtt Topologische groepen gtt Variétés kählériennes Kählerian manifolds Kähler-Mannigfaltigkeit (DE-588)4162978-4 gnd Unendlichdimensionale Mannigfaltigkeit (DE-588)4433823-5 gnd |
| topic_facet | Globale analyse Topologische groepen Variétés kählériennes Kählerian manifolds Kähler-Mannigfaltigkeit Unendlichdimensionale Mannigfaltigkeit |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009454375&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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