An introduction to the representation theory of groups:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
2014
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| Schriftenreihe: | Graduate studies in mathematics
155 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references |
| Beschreibung: | VI, 432 S. |
| ISBN: | 9781470409661 1470409666 |
Internformat
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Datensatz im Suchindex
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| adam_text | Titel: An introduction to the representation theory of groups
Autor: Kowalski, Emmanuel
Jahr: 2014
Contents Chapter 1. Introduction and motivation §1.1. Presentation §1.2. Four motivating statements §1.3. Prerequisites and notation Chapter 2. The language of representation theory §2.1. Basic language §2.2. Formalism: changing the space §2.3. Formalism: changing the group §2.4. Formalism: changing the field §2.5. Matrix representations §2.6. Examples §2.7. Some general results §2.8. Some Clifford theory §2.9. Conclusion Chapter 3. Variants §3.1. Representations of algebras §3.2. Representations of Lie algebras §3.3. Topological groups §3.4. Unitary representations Chapter 4. Linear representations of finite groups §4.1. Maschke’s Theorem 1 3 4 8 13 13 21 42 65 68 70 80 121 124 127 127 132 139 145 159 159 v
VI Contents §4.2. Applications of Maschke’s Theorem §4.3. Decomposition of representations §4.4. Harmonic analysis on finite groups §4.5. Finite abelian groups §4.6. The character table §4.7. Applications §4.8. Further topics Chapter 5. Abstract representation theory of compact groups §5.1. An example: the circle group §5.2. The Haar measure and the regular representation of a locally compact group §5.3. The analogue of the group algebra §5.4. The Peter-Weyl Theorem §5.5. Characters and matrix coefficients for compact groups §5.6. Some first examples Chapter 6. Applications of representations of compact groups §6.1. Compact Lie groups are matrix groups §6.2. The Frobenius-Schur indicator §6.3. The Larsen alternative §6.4. The hydrogen atom Chapter 7. Other groups: a few examples §7.1. Algebraic groups §7.2. Locally compact groups: general remarks §7.3. Locally compact abelian groups §7.4. A non-abelian example: SL 2 (R) Appendix A. Some useful facts §A.l. Algebraic integers §A.2. The spectral theorem §A.3. The Stone-Weierstrass Theorem Bibliography 163 169 190 200 208 240 262 269 269 272 288 294 304 310 319 319 324 332 344 355 355 369 371 376 409 409 414 420 421 Index 425
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| discipline | Mathematik |
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| language | English |
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| series | Graduate studies in mathematics |
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| spelling | Kowalski, Emmanuel 1969- Verfasser (DE-588)140530754 aut An introduction to the representation theory of groups Emmanuel Kowalski 2014 VI, 432 S. txt rdacontent n rdamedia nc rdacarrier Graduate studies in mathematics 155 Includes bibliographical references Gruppe Mathematik (DE-588)4022379-6 gnd rswk-swf Darstellungstheorie (DE-588)4148816-7 gnd rswk-swf Gruppe Mathematik (DE-588)4022379-6 s Darstellungstheorie (DE-588)4148816-7 s DE-604 Graduate studies in mathematics 155 (DE-604)BV009739289 155 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027632834&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kowalski, Emmanuel 1969- An introduction to the representation theory of groups Graduate studies in mathematics Gruppe Mathematik (DE-588)4022379-6 gnd Darstellungstheorie (DE-588)4148816-7 gnd |
| subject_GND | (DE-588)4022379-6 (DE-588)4148816-7 |
| title | An introduction to the representation theory of groups |
| title_auth | An introduction to the representation theory of groups |
| title_exact_search | An introduction to the representation theory of groups |
| title_full | An introduction to the representation theory of groups Emmanuel Kowalski |
| title_fullStr | An introduction to the representation theory of groups Emmanuel Kowalski |
| title_full_unstemmed | An introduction to the representation theory of groups Emmanuel Kowalski |
| title_short | An introduction to the representation theory of groups |
| title_sort | an introduction to the representation theory of groups |
| topic | Gruppe Mathematik (DE-588)4022379-6 gnd Darstellungstheorie (DE-588)4148816-7 gnd |
| topic_facet | Gruppe Mathematik Darstellungstheorie |
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