Elements of the theory of representations:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English Russian |
| Published: |
Berlin [u.a.]
Springer
1976
|
| Series: | Die Grundlehren der mathematischen Wissenschaften
220 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Aus dem Russ. übers. |
| Physical Description: | VIII, 315 S. |
| ISBN: | 3540074767 0387074767 |
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MARC
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| 245 | 1 | 0 | |a Elements of the theory of representations |c A. A. Kirillov |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1976 | |
| 300 | |a VIII, 315 S. | ||
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Record in the Search Index
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| adam_text | Table of Contents
First Part. Preliminary Facts
§ 1. Sets, Categories, Topology 1
1.1. Sets 1
1.2. Categories and Functors 3
1.3. The Elements of Topology 6
§ 2. Groups and Homogeneous Spaces 11
2.1. Transformation Groups and Abstract Groups 11
2.2. Homogeneous Spaces 15
2.3. Principal Types of Groups 16
2.4. Extensions of Groups 18
2.5. Cohomology of Groups 21
2.6. Topological Groups and Homogeneous Spaces 22
§ 3. Rings and Modules 24
3.1. Rings 25
3.2. Skew Fields 27
3.3. Modules over Rings 28
3.4. Linear Spaces 31
3.5. Algebras 32
§ 4. Elements of Functional Analysis 35
4.1. Linear Topological Spaces 35
4.2. Banach Algebras 44
4.3. C* Algebras 48
4.4. Commutative Operator Algebras 52
4.5. Continuous Sums of Hilbert Spaces and von Neumann Algebras 57
§ 5. Analysis on Manifolds 62
5.1. Manifolds 62
5.2. Vector Fields 68
5.3. Differential Forms 74
5.4. Bundles 77
§ 6. Lie Groups and Lie Algebras 83
6.1. Lie Groups 83
6.2. Lie Algebras 86
. 6.3. The Connection between Lie Groups and Lie Algebras .... 95
6.4. The Exponential Mapping 101
X Table of Contents
Second Part. Basic Concepts and Methods of the Theory of Representations
§7. Representations of Groups 108
7.1. Linear Representations 108
7.2. Representations of Topological Groups in Linear Topological
Spaces Ill
7.3. Unitary Representations 112
§8. Decomposition of Representations 115
8.1. Decomposition of Finite Representations 115
8.2. Irreducible Representations 119
8.3. Completely Reducible Representations 121
8.4. Decomposition of Unitary Representations 125
§ 9. Invariant Integration 129
9.1. Means and Invariant Measures 129
9.2. Applications to Compact Groups 133
9.3. Applications to Noncompact Groups 138
§ 10. Group Algebras 139
10.1. The Group Ring of a Finite Group 139
10.2. Group Algebras of Topological Groups 141
10.3. Application of Group C* Algebras 145
10.4. Group Algebras of Lie Groups 148
10.5. Representations of Lie Groups and their Group Algebras. . .152
§11. Characters 156
11.1. Characters of Finite Dimensional Representations 156
11.2. Characters of Infinite Dimensional Representations 160
11.3. Infinitesimal Characters 163
§12. Fourier Transforms and Duality 166
12.1. Commutative Groups 167
12.2. Compact Groups 173
12.3. Ring Groups and Duality for Finite Groups 177
12.4. Other Results 179
§13. Induced Representations 181
13.1. Induced Representations of Finite Groups 182
13.2. Unitary Induced Representations of Locally Compact Groups 187
13.3. Representations of Group Extensions 195
13.4. Induced Representations of Lie Groups and their Generaliza¬
tions 199
13.5. Intertwining Operators and Duality 205
13.6. Characters of Induced Representations 209
§ 14. Projective Representations 215
14.1. Projective Groups and Projective Representations 215
14.2. Schur s Theory 220
14.3. Projective Representations of Lie Groups 222
Table of Contents XI
§15. The Method of Orbits 226
15.1. The Co Adjoint Representation of a Lie Group 226
15.2. Homogeneous Symplectic Manifolds 231
15.3. Construction of an Irreducible Unitary Representation by an
Orbit 235
15.4. The Method of Orbits and Quantization of Hamiltonian
Mechanical Systems 241
15.5. Functorial Properties of the Correspondence between Orbits
and Representations 249
15.6. The Universal Formula for Characters and Plancherel Measures 251
15.7. Infinitesimal Characters and Orbits 256
Third Part. Various Examples
§ 16. Finite Groups 259
16.1. Harmonic Analysis on the Three Dimensional Cube 259
16.2. Representations of the Symmetric Group 262
16.3. Representations of the Group SL(2,Fq) 265
16.4. Vector Fields on Spheres 268
§ 17. Compact Groups 271
17.1. Harmonic Analysis on the Sphere 271
17.2. Representations of the Classical Compact Lie Groups .... 274
17.3. Spinor Representations of the Orthogonal Group 276
§ 18. Lie Groups and Lie Algebras 279
18.1. Representations of a Simple Three Dimensional Lie Algebra. . 279
18.2. The Weyl Algebra and Decomposition of Tensor Products . . 281
18.3. The Structure of the Enveloping Algebra U(q) for g = sI(2,C) • 283
18.4. Spinor Representations of the Symplectic Group 287
18.5. Representations of Triangular Matrix Groups 290
.§19. Examples of Wild Lie Groups 292
A Short Historical Sketch and a Guide to the Literature 297
Bibliography 302
Subject Index 310
|
| any_adam_object | 1 |
| author | Kirillov, Aleksandr A. 1936- |
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| dewey-full | 512/.22 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.22 |
| dewey-search | 512/.22 |
| dewey-sort | 3512 222 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| indexdate | 2024-07-09T15:38:09Z |
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| isbn | 3540074767 0387074767 |
| language | English Russian |
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| physical | VIII, 315 S. |
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| publishDate | 1976 |
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| series | Die Grundlehren der mathematischen Wissenschaften |
| series2 | Die Grundlehren der mathematischen Wissenschaften |
| spelling | Kirillov, Aleksandr A. 1936- Verfasser (DE-588)124974953 aut Élementy teorii predstavlenij Elements of the theory of representations A. A. Kirillov Berlin [u.a.] Springer 1976 VIII, 315 S. txt rdacontent n rdamedia nc rdacarrier Die Grundlehren der mathematischen Wissenschaften 220 Aus dem Russ. übers. Representations of groups Darstellungstheorie (DE-588)4148816-7 gnd rswk-swf Gruppentheorie (DE-588)4072157-7 gnd rswk-swf Darstellungstheorie (DE-588)4148816-7 s DE-604 Gruppentheorie (DE-588)4072157-7 s Die Grundlehren der mathematischen Wissenschaften 220 (DE-604)BV000000395 220 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001285906&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kirillov, Aleksandr A. 1936- Elements of the theory of representations Die Grundlehren der mathematischen Wissenschaften Representations of groups Darstellungstheorie (DE-588)4148816-7 gnd Gruppentheorie (DE-588)4072157-7 gnd |
| subject_GND | (DE-588)4148816-7 (DE-588)4072157-7 |
| title | Elements of the theory of representations |
| title_alt | Élementy teorii predstavlenij |
| title_auth | Elements of the theory of representations |
| title_exact_search | Elements of the theory of representations |
| title_full | Elements of the theory of representations A. A. Kirillov |
| title_fullStr | Elements of the theory of representations A. A. Kirillov |
| title_full_unstemmed | Elements of the theory of representations A. A. Kirillov |
| title_short | Elements of the theory of representations |
| title_sort | elements of the theory of representations |
| topic | Representations of groups Darstellungstheorie (DE-588)4148816-7 gnd Gruppentheorie (DE-588)4072157-7 gnd |
| topic_facet | Representations of groups Darstellungstheorie Gruppentheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001285906&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000395 |
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