Puig Frobenius Categories versus Brauer Blocks
2009
ISBN: 978-3-7643-9998-6
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark
The Grothendieck Group of the Frobenius Category of a Brauer Block
E-Book, Englisch, Band 274, 498 Seiten, eBook
Reihe: Progress in Mathematics
ISBN: 978-3-7643-9998-6
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark
This book contributes to important questions in modern representation theory of finite groups. It introduces and develops the abstract setting of the Frobenius categories and gives the application of the abstract setting to the blocks.
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Research
Autoren/Hrsg.
Weitere Infos & Material
Introduction.- 1. General notation and quoted results.- 2. Frobenius P-categories: the first definition.- 3. The Frobenius P-category of a block.- 4. Nilcentralized and selfcentralizing objects in Frobenius P-categories.- 5. Alperin fusions in Frobenius P-categories.- 6. Exterior quotient of a Frobenius P-category over the selfcentralizing objects.- 7 Nilcentralized and selfcentralizing Brauer pairs in blocks.- 8. Decompositions for Dade P-algebras.- 9. Polarizations for Dade P-algebras.- 10. A gluing theorem for Dade P-algebras.- 11. The nilcentralized chain k*-functor of a block.- 12. Quotients and normal subcategories in Frobenius P-categories.- 13. The hyperfocal subcategory of a Frobenius P-category.- 14. The Grothendieck groups of a Frobenius P-category.- 15. Reduction results for the Grothendieck groups.- 16. The local-global question: reduction to the simple groups.- 17. Localities associated with Frobenius P-categories.- 18. The localizers in a Frobenius P-category.- 19 Solvability for Frobenius P-categories.- 20 A perfect F-locality from a perfect Fsc-locality.- 21. Frobenius P-categories: the second definition.- 22. The basic F-locality.- 23. Narrowing the basic Fsc-locality.- 24. Looking for a perfect Fsc-locality.- Appendix.- References.- Index.
