Infinite-dimensional Lie Groups

Front Cover
American Mathematical Soc. - Mathematics - 415 pages
 

What people are saying - Write a review

We haven't found any reviews in the usual places.

Contents

Introduction
1
InfiniteDimensional Calculus
5
2 Integration
7
3 Generalized Lie groups
9
4 Rings and groups of linear mappings
14
5 Definition of differentiable mappings
19
6 Implicit function theorems
24
7 Ordinary differential equations Existence and regularity
27
2 Spectra of compact operators
161
3 Spectra of HilbertSchmidt operators
164
4 Adjoint actions and the HilleYoshida theorem
167
5 Elliptic differential operators
170
Normed Lie algebras
178
Several Subgroups of TM
181
2 Multivalued volume forms
185
3 Symplectic transformation groups
187

8 Examples of Sobolev chains
31
InfiniteDimensional Manifolds
35
2 Vector bundles and affine connections
40
3 Covariant exterior derivatives and Lie derivatives
43
4 Bmanifolds and gauge bundles
46
5 Frobenius theorems
50
6 ILHmanifolds and conformal structures
55
7 Groups of bounded operators and Grassmann manifolds
58
Chapter HI InfiniteDimensional Lie Groups
63
2 Finitedimensional subgroups finitecodimensional subgroups
68
3 Strong ILBLie groups
73
4 Lie algebras exponential mappings subgroups
78
5 Strong ILBLie groups are regular FLie groups
83
Geometrical Structures on Orbits
91
2 Geometrical structures defined by Lie algebras
95
3 Structures given by elliptic complexes
99
4 Several remarks
105
Fundamental Theorems for Differentiability
111
2 Bilateral ILBchains and formal adjoint operators
116
3 Differentiability and linear estimates
120
4 Linear mappings of FE into rSirEE
122
5 Differentiability of compositions
125
6 Continuity of the inverse
127
Groups of C Diffeomorphisms on Compact Manifolds
133
2 Groups of diffeomorphisms on compact manifolds
136
3 Several subgroups of VM
140
4 Subgroups of TM leaving a subset S invariant
142
5 Remarks on global hypoellipticity
146
6 Actions on differential forms
149
7 Conjugacy of compact subgroups
154
Linear Operators
159
4 Hamiltonian systems
191
5 Contact algebras and Poisson algebras
195
6 Contact transformations
198
7 Deformation of a regular contact structure
201
Smooth Extension Theorems
207
2 Subbundles defined by invariant bundle homomorphisms
211
3 The Frobenius theorem on strong ILBLie groups
215
4 Elementary smooth extension theorems on DM
217
5 A Smooth extension theorem for differential operators
220
6 The Frobenius theorem for finite codimensional Lie subalgebras
224
7 The implicit function theorem via Frobenius theorem
226
8 Existence of invariant connections and regularity of the exponential mapping
229
Group of Diffeomorphisms on Cotangent Bundles
233
2 Strong ILHLie group with the Lie algebra ETjS11
238
3 Infinitedimensional Lie groups with Lie algebra S1I
240
4 Regular FLie group with the Lie algebra ETjJ
244
5 Groups of paths and loops
247
6 Extensions by 2cocycles
251
Pseudodifferential Operators on Manifolds
255
Lie Algebra of Vector Fields
277
Quantizations
293
Poisson Manifolds and Quantum Groups
319
Weyl Manifolds
341
InfiniteDimensional Poisson Manifolds
361
Appendix I
381
Appendix II
389
Appendix III
395
References
403
Index
409
Copyright

Other editions - View all

Common terms and phrases

Bibliographic information