Infinite-dimensional Lie groups:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, R. I.
American Math. Soc.
1997
|
| Edition: | Transl. |
| Series: | Translations of mathematical monographs
158 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 415 S. |
| ISBN: | 0821845756 |
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MARC
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Record in the Search Index
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| adam_text | TRANSLATIONS OF MATHEMATICAL MONOGRAPHS VOLUME 158 INFINITE-DIMENSIONAL
LIE GROUPS HIDEKI OMORI TRANSLATED BY HIDEKI OMORI AMERICAN MATHEMATICAL
SOCIETY PROVIDENCE, RHODE ISLAND CONTENTS PREFACE TO THE ENGLISH EDITION
XI INTRODUCTION 1 CHAPTER I. INFINITE-DIMENSIONAL CALCULUS 5 §1
TOPOLOGICAL LINEAR SPACES 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 §8 EXAMPLES OF
SOBOLEV CHAINS 31 CHAPTER II. INFINITE-DIMENSIONAL MANIFOLDS 35 §1
F-MANIFOLDS, ILB-MANIFOLDS 35 §2 VECTOR BUNDLES AND AFFINE CONNECTIONS
40 §3 COVARIANT EXTERIOR DERIVATIVES AND LIE DERIVATIVES 43 §4
B-MANIFOLDS AND GAUGE BUNDLES 46 §5 FROBENIUS THEOREMS 50 §6
ILH-MANIFOLDS AND CONFORMAL STRUCTURES 55 §7 GROUPS OF BOUNDED OPERATORS
AND GRASSMANN MANIFOLDS 58 CHAPTER III. INFINITE-DIMENSIONAL LIE GROUPS
63 §1 REGULAR F-LIE GROUPS 63 §2 FINITE-DIMENSIONAL SUBGROUPS,
FINITE-CODIMENSIONAL SUBGROUPS 68 §3 STRONG ILB-LIE GROUPS 73 §4 LIE
ALGEBRAS, EXPONENTIAL MAPPINGS, SUBGROUPS 78 §5 STRONG ILB-LIE GROUPS
ARE REGULAR F-LIE GROUPS 83 CHAPTER IV. GEOMETRICAL STRUCTURES ON ORBITS
91 §1 ILB-REPRESENTATIONS OF STRONG ILB-LIE GROUPS 91 §2 GEOMETRICAL
STRUCTURES DEFINED BY LIE ALGEBRAS 95 §3 STRUCTURES GIVEN BY ELLIPTIC
COMPLEXES 99 §4 SEVERAL REMARKS 105 CHAPTER V. FUNDAMENTAL THEOREMS FOR
DIFFERENTIABILITY 111 §1 DIFFERENTIAL CALCULUS ON GEODESIC COORDINATE
111 §2 BILATERAL ILB-CHAINS AND FORMAL ADJOINT OPERATORS 116 §3
DIFFERENTIABILITY AND LINEAR ESTIMATES 120 CONTENTS §4 LINEAR MAPPINGS
OF R(E) INTO R(S(N^ E E)) 122 §5 DIFFERENTIABILITY OF COMPOSITIONS 125
§6 CONTINUITY OF THE INVERSE 127 CHAPTER VI. GROUPS OF C
DIFFEOMORPHISMS ON COMPACT MANIFOLDS 133 §1 INVARIANT CONNECTIONS AND
EULER S EQUATION OF GEODESIC FLOWS 133 §2 GROUPS OF DIFFEOMORPHISMS ON
COMPACT MANIFOLDS 136 §3 SEVERAL SUBGROUPS OF V{M) 140 §4 SUBGROUPS OF
V(M) LEAVING A SUBSET S INVARIANT 142 §5 REMARKS ON GLOBAL
HYPOELLIPTICITY 146 §6 ACTIONS ON DIFFERENTIAL FORMS 149 §7 CONJUGACY OF
COMPACT SUBGROUPS 154 CHAPTER VII. LINEAR OPERATORS 159 §1 OPERATOR
VALUED HOLOMORPHIC FUNCTIONS 159 §2 SPECTRA OF COMPACT OPERATORS 161 §3
SPECTRA OF HILBERT-SCHMIDT OPERATORS 164 §4 ADJOINT ACTIONS AND THE
HILLE-YOSHIDA THEOREM 167 §5 ELLIPTIC DIFFERENTIAL OPERATORS 170 §6
NORMED LIE ALGEBRAS 178 CHAPTER VIII. SEVERAL SUBGROUPS OF V{M) 181 §1
THE GROUP V DF ,(M) 181 §2 MULTIVALUED VOLUME FORMS 185 §3 SYMPLECTIC
TRANSFORMATION GROUPS 187 §4 HAMILTONIAN SYSTEMS 191 §5 CONTACT ALGEBRAS
AND POISSON ALGEBRAS 195 §6 CONTACT TRANSFORMATIONS 198 §7 DEFORMATION
OF A REGULAR CONTACT STRUCTURE 201 CHAPTER IX. SMOOTH EXTENSION THEOREMS
207 §1 VECTOR BUNDLES AND INVARIANT HOMOMORPHISMS 207 §2 SUBBUNDLES
DEFINED BY INVARIANT BUNDLE HOMOMORPHISMS 211 §3 THE FROBENIUS THEOREM
ON STRONG ILB-LIE GROUPS 215 §4 ELEMENTARY, SMOOTH EXTENSION THEOREMS ON
V(M) 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
CHAPTER X. GROUP OF DIFFEOMORPHISMS ON COTANGENT BUNDLES 233 §1
INFINITE-DIMENSIONAL LIE ALGEBRAS IN GENERAL RELATIVITY 233 §2 STRONG
ILH-LIE GROUP WITH THE LIE ALGEBRA T, 1 (T^)/E 1 - 1 (T^) 238 §3
INFINITE-DIMENSIONAL LIE GROUPS WITH LIE ALGEBRA E 1 (TJ^) 240 §4
REGULAR F-LIE GROUP WITH THE LIE ALGEBRA E^TJ,) 244 §5 GROUPS OF PATHS
AND LOOPS 247 §6 EXTENSIONS BY 2-COCYCLES 251 CHAPTER XI.
PSEUDODIFFEREHTIAL OPERATORS ON MANIFOLDS 255 CONTENTS IX §1
PSEUDODIFFERENTIAL OPERATORS ON COMPACT MANIFOLDS 255 §2 PRODUCTS OF
PSEUDODIFFERENTIAL OPERATORS 259 §3 SEVERAL REMARKS ON
PSEUDODIFFERENTIAL OPERATORS 262 §4 ALGEBRAS AND LIE ALGEBRAS OF
PSEUDODIFFERENTIAL OPERATORS 266 §5 FOURIER INTEGRAL OPERATORS 272
CHAPTER XII. LIE ALGEBRA OF VECTOR FIELDS 277 §1 A GENERALIZATION OF THE
PS-THEOREM 277 §2 ORBITS OF LIE ALGEBRAS 282 §3 NORMAL FORMS OF VECTOR
FIELDS 284 §4 THE PS-THEOREM FOR LIE ALGEBRAS LEAVING EXPANSIVE SUBSETS
INVARI- ANT 288 CHAPTER XIII. QUANTIZATIONS 293 §1 THE CORRESPONDENCE
PRINCIPLE 294 §2 LINEAR OPERATORS ON SOBOLEV CHAINS 296 §3 QUANTIZED
CONTACT ALGEBRAS 300 §4 SEVERAL ALGEBRAIC TOOLS 305 §5 DEFORMATION
QUANTIZATION OF POISSON ALGEBRAS 309 §6 SEVERAL REMARKS AND QUANTIZED
DARBOUX THEOREM 314 CHAPTER XIV. POISSON MANIFOLDS AND QUANTUM GROUPS
319 §1 EXAMPLES OF DEFORMATION QUANTIZED POISSON ALGEBRA 319 §2 QUANTUM
GROUPS 325 §3 QUANTUM SU Q (2), SU Q (L, 1) 328 §4 DEFORMATION
QUANTIZATION OF (S 2 ,DV) 33 4 §5 REMARKS ON EXACT DEFORMATION
QUANTIZATIONS 337 CHAPTER XV. WEYL MANIFOLDS 341 §1 WEYL ALGEBRAS,
CONTACT WEYL ALGEBRAS 341 §2 WEYL FUNCTIONS 345 §3 WEYL DIFFEOMORPHISMS
347 §4 WEYL MANIFOLDS 350 §5 SEVERAL STRUCTURES ON WEYL MANIFOLDS 355
CHAPTER XVI. INFINITE-DIMENSIONAL POISSON MANIFOLDS 361 §1 EQUATION OF
PERFECT FLUID AND GEODESIES 361 §2 SMOOTH FUNCTIONS ON SOBOLEV CHAINS
365 §3 COTANGENT BUNDLES OF SOBOLEV MANIFOLDS 368 §4 STRONG ILH-LIE
GROUPS AS SOBOLEV MANIFOLDS 372 §5 THE STAR-PRODUCT ON T 374 APPENDIX I
381 APPENDIX II 389 APPENDIX III 395 REFERENCES 403 INDEX 409
|
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| author | Ōmori, Hideki 1938- |
| author_GND | (DE-588)104334339 |
| author_facet | Ōmori, Hideki 1938- |
| author_role | aut |
| author_sort | Ōmori, Hideki 1938- |
| author_variant | h ō hō |
| building | Verbundindex |
| bvnumber | BV024975324 |
| classification_rvk | SK 340 |
| ctrlnum | (OCoLC)246828232 (DE-599)BVBBV024975324 |
| dewey-full | 514.223 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
| dewey-raw | 514.223 |
| dewey-search | 514.223 |
| dewey-sort | 3514.223 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | Transl. |
| format | Book |
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| indexdate | 2024-07-09T22:24:53Z |
| institution | BVB |
| isbn | 0821845756 |
| language | English |
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| physical | XII, 415 S. |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | American Math. Soc. |
| record_format | marc |
| series | Translations of mathematical monographs |
| series2 | Translations of mathematical monographs |
| spelling | Ōmori, Hideki 1938- Verfasser (DE-588)104334339 aut Infinite-dimensional Lie groups Hideki Omori Transl. Providence, R. I. American Math. Soc. 1997 XII, 415 S. txt rdacontent n rdamedia nc rdacarrier Translations of mathematical monographs 158 Unendlichdimensionale Lie-Gruppe (DE-588)4530098-7 gnd rswk-swf Unendlichdimensionale Lie-Gruppe (DE-588)4530098-7 s DE-604 Translations of mathematical monographs 158 (DE-604)BV000002394 158 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=019642787&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ōmori, Hideki 1938- Infinite-dimensional Lie groups Translations of mathematical monographs Unendlichdimensionale Lie-Gruppe (DE-588)4530098-7 gnd |
| subject_GND | (DE-588)4530098-7 |
| title | Infinite-dimensional Lie groups |
| title_auth | Infinite-dimensional Lie groups |
| title_exact_search | Infinite-dimensional Lie groups |
| title_full | Infinite-dimensional Lie groups Hideki Omori |
| title_fullStr | Infinite-dimensional Lie groups Hideki Omori |
| title_full_unstemmed | Infinite-dimensional Lie groups Hideki Omori |
| title_short | Infinite-dimensional Lie groups |
| title_sort | infinite dimensional lie groups |
| topic | Unendlichdimensionale Lie-Gruppe (DE-588)4530098-7 gnd |
| topic_facet | Unendlichdimensionale Lie-Gruppe |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=019642787&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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