Modular representation theory of finite groups
Representation theory studies maps from groups into the general linear group of a finite-dimensional vector space. For finite groups the theory comes in two distinct flavours. In the 'semisimple case' (for example over the field of complex numbers) one can use character theory to completel...
محفوظ في:
| المؤلف الرئيسي: | |
|---|---|
| التنسيق: | Livre numérique |
| اللغة: | Anglais |
| منشور في: |
London :
Springer London
2013.
Cham : Springer Nature |
| الموضوعات: | |
| الوصول للمادة أونلاين: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| ملاحظة: |
Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Modular representation theory of finite groups, Peter Schneider, 2013, Dordrecht, Springer, 1 volume (VIII-178 pages), 978-1-447-14831-9 • Modular Representation Theory of Finite Groups, Texte imprimé, 9781447148333 • Modular Representation Theory of Finite Groups, Texte imprimé, 9781447173625 |
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| 001 | 949545 | ||
| 008 | 130325s2013 xx ||| |||| 00| 0 eng d | ||
| 009 | PPN168294338 | ||
| 020 | |a 9781447148326 | ||
| 020 | |a 9781447148326 | ||
| 041 | 0 | |a eng | |
| 082 | |a 512.46 | ||
| 100 | 1 | |a Schneider, Peter, |d 1953-...., |c mathématicien. | |
| 245 | 1 | 0 | |a Modular representation theory of finite groups |c by Peter Schneider. |
| 260 | |a London : |b Springer London. | ||
| 260 | |a Cham : |b Springer Nature, |c 2013. | ||
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 505 | 0 | |a Prerequisites in module theory -- The Cartan{Brauer triangle -- The Brauer character -- Green's theory of indecomposable modules -- Blocks. | |
| 506 | |a Accès en ligne pour les établissements français bénéficiaires des licences nationales | ||
| 506 | |a Accès soumis à abonnement pour tout autre établissement | ||
| 506 | |a Conditions particulières de réutilisation pour les bénéficiaires des licences nationales. chttps://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 | ||
| 520 | |a Representation theory studies maps from groups into the general linear group of a finite-dimensional vector space. For finite groups the theory comes in two distinct flavours. In the 'semisimple case' (for example over the field of complex numbers) one can use character theory to completely understand the representations. This by far is not sufficient when the characteristic of the field divides the order of the group. Modular representation theory of finite groups comprises this second situation. Many additional tools are needed for this case. To mention some, there is the systematic use of Grothendieck groups leading to the Cartan matrix and the decomposition matrix of the group as well as Green's direct analysis of indecomposable representations. There is also the strategy of writing the category of all representations as the direct product of certain subcategories, the so-called 'blocks' of the group. Brauer's work then establishes correspondences between the blocks of theoriginal group and blocks of certain subgroups the philosophy being that one is thereby reduced to a simpler situation. In particular, one can measure how nonsemisimple a category a block is by the size and structure of its so-called 'defect group'. All these concepts are made explicit for the example of the special linear group of two-by-two matrices over a finite prime field. Although the presentation is strongly biased towards the module theoretic point of view an attempt is made to strike a certain balance by also showing the reader the group theoretic approach. In particular, in the case of defect groups a detailed proof of the equivalence of the two approaches is given. This book aims to familiarize students at the masters level with the basic results, tools, and techniques of a beautiful and important algebraic theory. Some basic algebra together with the semisimple case are assumed to be known, although all facts to be used are restated (without proofs) in the text. Otherwise the book is entirely self-contained. | ||
| 650 | |a Représentations modulaires de groupes | ||
| 650 | |a Groupes finis | ||
| 776 | 0 | |0 175007128 |t Modular representation theory of finite groups |f Peter Schneider |d 2013 |c Dordrecht |n Springer |p 1 volume (VIII-178 pages) |z 978-1-447-14831-9 | |
| 776 | 0 | |t Modular Representation Theory of Finite Groups |b Texte imprimé |z 9781447148333 | |
| 776 | 0 | |t Modular Representation Theory of Finite Groups |b Texte imprimé |z 9781447173625 | |
| 856 | 4 | |q PDF |u https://doi.org/10.1007/978-1-4471-4832-6 |z Accès sur la plateforme de l'éditeur | |
| 856 | 4 | |u https://revue-sommaire.istex.fr/ark:/67375/8Q1-7PQFGWMC-4 |z Accès sur la plateforme Istex | |
| 856 | 4 | |5 452349901:748125396 |u https://ezproxy.univ-orleans.fr/login?url=https://dx.doi.org/10.1007/978-1-4471-4832-6 |z Accès Université d'Orléans | |
| 856 | 4 | |5 180339901:751580155 |u https://ezproxy.insa-cvl.fr/login?qurl=https://dx.doi.org/10.1007/978-1-4471-4832-6 |z Accès INSA CVL | |
| 997 | |0 949545 |1 Livre numérique |a Ressource numérique |b INSA |b ENSA |c 0/Bibliothèque numérique/ |c 1/Bibliothèque numérique/Autre ressource numérique/ | ||