Local representation theory: modular representations as an introduction to the local representation theory of finite groups
The aim of this text is to present some of the key results in the representation theory of finite groups. In order to keep the account reasonably elementary, so that it can be used for graduate-level courses, Professor Alperin has concentrated on local representation theory, emphasising module theor...
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| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
1986
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| Schriftenreihe: | Cambridge studies in advanced mathematics
11 |
| Schlagworte: | |
| Online-Zugang: | BSB01 FHN01 UBR01 Volltext |
| Zusammenfassung: | The aim of this text is to present some of the key results in the representation theory of finite groups. In order to keep the account reasonably elementary, so that it can be used for graduate-level courses, Professor Alperin has concentrated on local representation theory, emphasising module theory throughout. In this way many deep results can be obtained rather quickly. After two introductory chapters, the basic results of Green are proved, which in turn lead in due course to Brauer's First Main Theorem. A proof of the module form of Brauer's Second Main Theorem is then presented, followed by a discussion of Feit's work connecting maps and the Green correspondence. The work concludes with a treatment, new in part, of the Brauer-Dade theory. As a text, this book contains ample material for a one semester course. Exercises are provided at the end of most sections; the results of some are used later in the text. Representation theory is applied in number theory, combinatorics and in many areas of algebra. This book will serve as an excellent introduction to those interested in the subject itself or its applications |
| Beschreibung: | Title from publisher's bibliographic system (viewed on 05 Oct 2015) |
| Beschreibung: | 1 online resource (x, 178 Seiten) |
| ISBN: | 9780511623592 |
| DOI: | 10.1017/CBO9780511623592 |
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Datensatz im Suchindex
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| author | Alperin, Jonathan L. 1937- |
| author_GND | (DE-588)141230835 |
| author_facet | Alperin, Jonathan L. 1937- |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
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| discipline | Mathematik |
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| id | DE-604.BV043940121 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:12Z |
| institution | BVB |
| isbn | 9780511623592 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029349091 |
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| publishDate | 1986 |
| publishDateSearch | 1986 |
| publishDateSort | 1986 |
| publisher | Cambridge University Press |
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| series | Cambridge studies in advanced mathematics |
| series2 | Cambridge studies in advanced mathematics |
| spelling | Alperin, Jonathan L. 1937- Verfasser (DE-588)141230835 aut Local representation theory modular representations as an introduction to the local representation theory of finite groups J.L. Alperin Cambridge Cambridge University Press 1986 1 online resource (x, 178 Seiten) txt rdacontent c rdamedia cr rdacarrier Cambridge studies in advanced mathematics 11 Title from publisher's bibliographic system (viewed on 05 Oct 2015) The aim of this text is to present some of the key results in the representation theory of finite groups. In order to keep the account reasonably elementary, so that it can be used for graduate-level courses, Professor Alperin has concentrated on local representation theory, emphasising module theory throughout. In this way many deep results can be obtained rather quickly. After two introductory chapters, the basic results of Green are proved, which in turn lead in due course to Brauer's First Main Theorem. A proof of the module form of Brauer's Second Main Theorem is then presented, followed by a discussion of Feit's work connecting maps and the Green correspondence. The work concludes with a treatment, new in part, of the Brauer-Dade theory. As a text, this book contains ample material for a one semester course. Exercises are provided at the end of most sections; the results of some are used later in the text. Representation theory is applied in number theory, combinatorics and in many areas of algebra. This book will serve as an excellent introduction to those interested in the subject itself or its applications Finite groups Modular representations of groups Gruppentheorie (DE-588)4072157-7 gnd rswk-swf Darstellungstheorie (DE-588)4148816-7 gnd rswk-swf Modulare Darstellung (DE-588)4311996-7 gnd rswk-swf Endliche Gruppe (DE-588)4014651-0 gnd rswk-swf Endliche Gruppe (DE-588)4014651-0 s Modulare Darstellung (DE-588)4311996-7 s DE-604 Darstellungstheorie (DE-588)4148816-7 s Gruppentheorie (DE-588)4072157-7 s Erscheint auch als Druck-Ausgabe 978-0-521-30660-7 Erscheint auch als Druck-Ausgabe 978-0-521-44926-7 Cambridge studies in advanced mathematics 11 (DE-604)BV044781283 11 https://doi.org/10.1017/CBO9780511623592 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Alperin, Jonathan L. 1937- Local representation theory modular representations as an introduction to the local representation theory of finite groups Cambridge studies in advanced mathematics Finite groups Modular representations of groups Gruppentheorie (DE-588)4072157-7 gnd Darstellungstheorie (DE-588)4148816-7 gnd Modulare Darstellung (DE-588)4311996-7 gnd Endliche Gruppe (DE-588)4014651-0 gnd |
| subject_GND | (DE-588)4072157-7 (DE-588)4148816-7 (DE-588)4311996-7 (DE-588)4014651-0 |
| title | Local representation theory modular representations as an introduction to the local representation theory of finite groups |
| title_auth | Local representation theory modular representations as an introduction to the local representation theory of finite groups |
| title_exact_search | Local representation theory modular representations as an introduction to the local representation theory of finite groups |
| title_full | Local representation theory modular representations as an introduction to the local representation theory of finite groups J.L. Alperin |
| title_fullStr | Local representation theory modular representations as an introduction to the local representation theory of finite groups J.L. Alperin |
| title_full_unstemmed | Local representation theory modular representations as an introduction to the local representation theory of finite groups J.L. Alperin |
| title_short | Local representation theory |
| title_sort | local representation theory modular representations as an introduction to the local representation theory of finite groups |
| title_sub | modular representations as an introduction to the local representation theory of finite groups |
| topic | Finite groups Modular representations of groups Gruppentheorie (DE-588)4072157-7 gnd Darstellungstheorie (DE-588)4148816-7 gnd Modulare Darstellung (DE-588)4311996-7 gnd Endliche Gruppe (DE-588)4014651-0 gnd |
| topic_facet | Finite groups Modular representations of groups Gruppentheorie Darstellungstheorie Modulare Darstellung Endliche Gruppe |
| url | https://doi.org/10.1017/CBO9780511623592 |
| volume_link | (DE-604)BV044781283 |
| work_keys_str_mv | AT alperinjonathanl localrepresentationtheorymodularrepresentationsasanintroductiontothelocalrepresentationtheoryoffinitegroups |