Linear Representations of Finite Groups:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, Heidelberg, Berlin
Springer New York
[1977]
|
| Schriftenreihe: | Graduate texts in mathematics
42 |
| Schlagworte: | |
| Online-Zugang: | FUBA1 Volltext |
| Beschreibung: | This book consists of three parts, rather different in level and purpose: The first part was originally written for quantum chemists. It describes the correspondence, due to Frobenius, between linear representations and charac ters. This is a fundamental result, of constant use in mathematics as well as in quantum chemistry or physics. I have tried to give proofs as elementary as possible, using only the definition of a group and the rudiments of linear algebra. The examples (Chapter 5) have been chosen from those useful to chemists. The second part is a course given in 1966 to second-year students of I'Ecoie Normale. It completes the first on the following points: (a) degrees of representations and integrality properties of characters (Chapter 6); (b) induced representations, theorems of Artin and Brauer, and applications (Chapters 7-11); (c) rationality questions (Chapters 12 and 13). The methods used are those of linear algebra (in a wider sense than in the first part): group algebras, modules, noncommutative tensor products, semisimple algebras. The third part is an introduction to Brauer theory: passage from characteristic 0 to characteristic p (and conversely). I have freely used the language of abelian categories (projective modules, Grothendieck groups), which is well suited to this sort of question. The principal results are: (a) The fact that the decomposition homomorphism is surjective: all irreducible representations in characteristic p can be lifted "virtually" (i.e., in a suitable Grothendieck group) to characteristic O. |
| Beschreibung: | 1 Online-Ressource (x, 170 Seiten) |
| ISBN: | 9781468494587 |
| ISSN: | 0072-5285 |
| DOI: | 10.1007/978-1-4684-9458-7 |
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Datensatz im Suchindex
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| author | Serre, Jean-Pierre 1926- |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.2 |
| dewey-search | 512.2 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4684-9458-7 |
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| id | DE-604.BV042421225 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:08Z |
| institution | BVB |
| isbn | 9781468494587 |
| issn | 0072-5285 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027856642 |
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| publishDate | 1977 |
| publishDateSearch | 1977 |
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| series | Graduate texts in mathematics |
| series2 | Graduate Texts in Mathematics |
| spelling | Serre, Jean-Pierre 1926- Verfasser (DE-588)142283126 aut Représentations linéaires des groupes finis Linear Representations of Finite Groups Jean-Pierre Serre ; translated from the French by ... New York, Heidelberg, Berlin Springer New York [1977] 1 Online-Ressource (x, 170 Seiten) txt rdacontent c rdamedia cr rdacarrier Graduate Texts in Mathematics 42 0072-5285 This book consists of three parts, rather different in level and purpose: The first part was originally written for quantum chemists. It describes the correspondence, due to Frobenius, between linear representations and charac ters. This is a fundamental result, of constant use in mathematics as well as in quantum chemistry or physics. I have tried to give proofs as elementary as possible, using only the definition of a group and the rudiments of linear algebra. The examples (Chapter 5) have been chosen from those useful to chemists. The second part is a course given in 1966 to second-year students of I'Ecoie Normale. It completes the first on the following points: (a) degrees of representations and integrality properties of characters (Chapter 6); (b) induced representations, theorems of Artin and Brauer, and applications (Chapters 7-11); (c) rationality questions (Chapters 12 and 13). The methods used are those of linear algebra (in a wider sense than in the first part): group algebras, modules, noncommutative tensor products, semisimple algebras. The third part is an introduction to Brauer theory: passage from characteristic 0 to characteristic p (and conversely). I have freely used the language of abelian categories (projective modules, Grothendieck groups), which is well suited to this sort of question. The principal results are: (a) The fact that the decomposition homomorphism is surjective: all irreducible representations in characteristic p can be lifted "virtually" (i.e., in a suitable Grothendieck group) to characteristic O. Mathematics Group theory Group Theory and Generalizations Mathematik Lineare Darstellung (DE-588)4167703-1 gnd rswk-swf Endliche Gruppe (DE-588)4014651-0 gnd rswk-swf Gruppentheorie (DE-588)4072157-7 gnd rswk-swf Darstellungstheorie (DE-588)4148816-7 gnd rswk-swf Endliche Gruppe (DE-588)4014651-0 s Lineare Darstellung (DE-588)4167703-1 s 1\p DE-604 Darstellungstheorie (DE-588)4148816-7 s 2\p DE-604 Gruppentheorie (DE-588)4072157-7 s 3\p DE-604 Erscheint auch als Druck-Ausgabe 978-1-4684-9460-0 (DE-604)BV006363723 Graduate texts in mathematics 42 (DE-604)BV035421258 42 https://doi.org/10.1007/978-1-4684-9458-7 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Serre, Jean-Pierre 1926- Linear Representations of Finite Groups Graduate texts in mathematics Mathematics Group theory Group Theory and Generalizations Mathematik Lineare Darstellung (DE-588)4167703-1 gnd Endliche Gruppe (DE-588)4014651-0 gnd Gruppentheorie (DE-588)4072157-7 gnd Darstellungstheorie (DE-588)4148816-7 gnd |
| subject_GND | (DE-588)4167703-1 (DE-588)4014651-0 (DE-588)4072157-7 (DE-588)4148816-7 |
| title | Linear Representations of Finite Groups |
| title_alt | Représentations linéaires des groupes finis |
| title_auth | Linear Representations of Finite Groups |
| title_exact_search | Linear Representations of Finite Groups |
| title_full | Linear Representations of Finite Groups Jean-Pierre Serre ; translated from the French by ... |
| title_fullStr | Linear Representations of Finite Groups Jean-Pierre Serre ; translated from the French by ... |
| title_full_unstemmed | Linear Representations of Finite Groups Jean-Pierre Serre ; translated from the French by ... |
| title_short | Linear Representations of Finite Groups |
| title_sort | linear representations of finite groups |
| topic | Mathematics Group theory Group Theory and Generalizations Mathematik Lineare Darstellung (DE-588)4167703-1 gnd Endliche Gruppe (DE-588)4014651-0 gnd Gruppentheorie (DE-588)4072157-7 gnd Darstellungstheorie (DE-588)4148816-7 gnd |
| topic_facet | Mathematics Group theory Group Theory and Generalizations Mathematik Lineare Darstellung Endliche Gruppe Gruppentheorie Darstellungstheorie |
| url | https://doi.org/10.1007/978-1-4684-9458-7 |
| volume_link | (DE-604)BV035421258 |
| work_keys_str_mv | AT serrejeanpierre representationslineairesdesgroupesfinis AT serrejeanpierre linearrepresentationsoffinitegroups |