Frobenius Categories versus Brauer Blocks : the Grothendieck group of the Frobenius category of a Brauer block
This book contributes to important questions in the representation theory of finite groups over fields of positive characteristic an area of research initiated by Richard Brauer sixty years ago with the introduction of the blocks of characters. On the one hand, it introduces and develops the abstrac...
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| Autor principal: | |
|---|---|
| Formato: | Livre numérique |
| Idioma: | Anglais |
| Publicado em: |
Basel :
Birkhäuser Basel
[20..].
Cham : Springer Nature |
| Edição: | 1st ed. 2009. |
| Colecção: | Progress in Mathematics
274 |
| Assuntos: | |
| Acesso em linha: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Nota: |
L'impression du document génère 480 p. Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Frobenius categories versus Brauer blocks, the Grothendieck group of the Frobenius category of a Brauer block, Lluís Puig, Basel, Birkhäuser, 2009, 1 vol. (498 p.), Progress in mathematics, 978-3-7643-9997-9 • Frobenius Categories versus Brauer Blocks, Texte imprimé, 9783034600156 • Frobenius categories versus Brauer blocks, the Grothendieck group of the Frobenius category of a Brauer block, Lluís Puig, Basel, Birkhäuser, 2009, 1 vol. (498 p.), Progress in mathematics, 978-3-7643-9997-9 |
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| 009 | PPN136307256 | ||
| 020 | |a 9783764399986 | ||
| 041 | 0 | |a eng | |
| 082 | |a 512.2 | ||
| 084 | |a 20C11. 2000 | ||
| 100 | 1 | |a Puig, Luis, |d 1943-...., |c mathématicien. | |
| 245 | 1 | 0 | |a Frobenius Categories versus Brauer Blocks : |b the Grothendieck group of the Frobenius category of a Brauer block |c Lluís Puig. |
| 250 | |a 1st ed. 2009. | ||
| 260 | |a Basel : |b Birkhäuser Basel. | ||
| 260 | |a Cham : |b Springer Nature, |c [20..]. | ||
| 490 | 0 | |a Progress in Mathematics |v 274 |x 2296-505X | |
| 500 | |a L'impression du document génère 480 p. | ||
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 505 | 1 | |a General notation and quoted results Frobenius P-categories: the first definition The Frobenius P-category of a block Nilcentralized, selfcentralizing and intersected objects in Frobenius P-categories Alperin fusions in Frobenius P-categories Exterior quotient of a Frobenius P-category over the selfcentralizing objects Nilcentralized and selfcentralizing Brauer pairs in blocks Decompositions for Dade P-algebras Polarizations for Dade P-algebras A gluing theorem for Dade P-algebras The nilcentralized chain k*-functor of a block Quotients and normal subcategories in Frobenius P-categories The hyperfocal subcategory of a Frobenius P-category The Grothendieck groups of a Frobenius P-category Reduction results for Grothendieck groups The local-global question: reduction to the simple groups Localities associated with a Frobenius P-category The localizers in a Frobenius P-category Solvability for Frobenius P-categories A perfect F-locality from a perfect Fsc -locality Frobenius P-categories: the second definition The basic F-locality Narrowing the basic Fsc-locality Looking for a perfect Fsc-locality | |
| 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. https://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 | ||
| 520 | |a This book contributes to important questions in the representation theory of finite groups over fields of positive characteristic an area of research initiated by Richard Brauer sixty years ago with the introduction of the blocks of characters. On the one hand, it introduces and develops the abstract setting of the Frobenius categories also called the Saturated fusion systems in the literature created by the author fifteen years ago for a better understanding of what was loosely called the local theory of a finite group around a prime number p or, later, around a Brauer block, and for the purpose of an eventual classification a reasonable concept of simple Frobenius category arises. On the other hand, the book develops this abstract setting in parallel with its application to the Brauer blocks, giving the detailed translation of any abstract concept in the particular context of the blocks. One of the new features in this direction is a framework for a deeper understanding of one of the central open problems in modular representation theory, known as Alperin s Weight Conjecture (AWC). Actually, this new framework suggests a more general form of AWC, and a significant result of the book is a reduction theorem of this form of AWC to quasi-simple groups. Although this book is a research monograph, all the arguments are widely developed to make it accessible to the interested graduate students and, at the same time, to put them on the verge of the research on this new subject: the third part of the book on the localities associated to a Frobenius category gives some insight on the open question about the existence and the uniquenes of a perfect locality also called centric linking system in the literature. We have developed a long introduction to explain our purpose and to provide a guideline for the reader throughout the twenty four sections. A systematic appendix on the cohomology of categories completes the book | ||
| 650 | |a Représentations de groupes | ||
| 650 | |a Groupes de Frobenius | ||
| 650 | |a Brauer, Groupe de | ||
| 650 | |a Groupes de Grothendieck | ||
| 776 | 0 | |0 132521369 |t Frobenius categories versus Brauer blocks |o the Grothendieck group of the Frobenius category of a Brauer block |f Lluís Puig |c Basel |n Birkhäuser |d 2009 |p 1 vol. (498 p.) |s Progress in mathematics |z 978-3-7643-9997-9 | |
| 776 | 0 | |t Frobenius Categories versus Brauer Blocks |b Texte imprimé |z 9783034600156 | |
| 776 | 0 | |0 132521369 |t Frobenius categories versus Brauer blocks |o the Grothendieck group of the Frobenius category of a Brauer block |f Lluís Puig |c Basel |n Birkhäuser |d 2009 |p 1 vol. (498 p.) |s Progress in mathematics |z 978-3-7643-9997-9 | |
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| 997 | |0 941733 |1 Livre numérique |a Ressource numérique |b INSA |b ENSA |c 0/Bibliothèque numérique/ |c 1/Bibliothèque numérique/Autre ressource numérique/ | ||