000			04614nam a22003735i 4500
001			309824
003			MX-SnUAN
005			20160429160326.0
007			cr nn 008mamaa
008			150903s2009 sz | o |||| 0|eng d
020			_a9783764399986 _99783764399986
024	7		_a10.1007/9783764399986 _2doi
035			_avtls000363035
039		9	_a201509030651 _bVLOAD _c201405070338 _dVLOAD _y201402211137 _zstaff
040			_aMX-SnUAN _bspa _cMX-SnUAN _erda
050		4	_aQA174-183
100	1		_aPuig, Lluís. _eautor _9350285
245	1	0	_aFrobenius Categories versus Brauer Blocks : _bThe Grothendieck Group of the Frobenius Category of a Brauer Block / _cby Lluís Puig.
264		1	_aBasel : _bBirkhäuser Basel, _c2009.
300			_brecurso en línea.
336			_atexto _btxt _2rdacontent
337			_acomputadora _bc _2rdamedia
338			_arecurso en línea _bcr _2rdacarrier
347			_aarchivo de texto _bPDF _2rda
490	0		_aProgress in Mathematics ; _v274
500			_aSpringer eBooks
505	0		_aGeneral 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.
520			_aThis 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.
590			_aPara consulta fuera de la UANL se requiere clave de acceso remoto.
710	2		_aSpringerLink (Servicio en línea) _9299170
776	0	8	_iEdición impresa: _z9783764399979
856	4	0	_uhttp://remoto.dgb.uanl.mx/login?url=http://dx.doi.org/10.1007/978-3-7643-9998-6 _zConectar a Springer E-Books (Para consulta externa se requiere previa autentificación en Biblioteca Digital UANL)
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999			_c309824 _d309824