Frobenius Categories versus Brauer Blocks PDF Download
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Author: Lluís Puig
Publisher: Springer Science & Business Media
ISBN: 3764399988
Category : Mathematics
Languages : en
Pages : 481
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Book Description
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.
Author: Lluís Puig
Publisher: Springer Science & Business Media
ISBN: 3764399988
Category : Mathematics
Languages : en
Pages : 481
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Book Description
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.
Author: Lluís Puig
Publisher: Birkhäuser
ISBN: 9783034600156
Category : Mathematics
Languages : en
Pages : 498
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Book Description
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.
Author: J. Oesterlé Edited by H. Bass (A. Weinstein)
Publisher:
ISBN: 9781282333215
Category :
Languages : en
Pages :
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Book Description
Author: Lluís Puig
Publisher: Birkhäuser
ISBN: 9783764399979
Category : Mathematics
Languages : en
Pages : 498
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Book Description
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.
Author: Benjamin Sambale
Publisher: Springer
ISBN: 3319120069
Category : Mathematics
Languages : en
Pages : 243
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Book Description
Providing a nearly complete selection of up-to-date methods and results on block invariants with respect to their defect groups, this book covers the classical theory pioneered by Brauer, the modern theory of fusion systems introduced by Puig, the geometry of numbers developed by Minkowski, the classification of finite simple groups, and various computer assisted methods. In a powerful combination, these tools are applied to solve many special cases of famous open conjectures in the representation theory of finite groups. Most of the material is drawn from peer-reviewed journal articles, but there are also new previously unpublished results. In order to make the text self-contained, detailed proofs are given whenever possible. Several tables add to the text's usefulness as a reference. The book is aimed at experts in group theory or representation theory who may wish to make use of the presented ideas in their research.
Author: Michael Aschbacher
Publisher: Cambridge University Press
ISBN: 1107601002
Category : Mathematics
Languages : en
Pages : 329
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Book Description
A fusion system over a p-group S is a category whose objects form the set of all subgroups of S, whose morphisms are certain injective group homomorphisms, and which satisfies axioms first formulated by Puig that are modelled on conjugacy relations in finite groups. The definition was originally motivated by representation theory, but fusion systems also have applications to local group theory and to homotopy theory. The connection with homotopy theory arises through classifying spaces which can be associated to fusion systems and which have many of the nice properties of p-completed classifying spaces of finite groups. Beginning with a detailed exposition of the foundational material, the authors then proceed to discuss the role of fusion systems in local finite group theory, homotopy theory and modular representation theory. This book serves as a basic reference and as an introduction to the field, particularly for students and other young mathematicians.
Author:
Publisher: ScholarlyEditions
ISBN: 1464966354
Category : Mathematics
Languages : en
Pages : 395
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Book Description
Issues in Algebra, Geometry, and Topology / 2011 Edition is a ScholarlyEditions™ eBook that delivers timely, authoritative, and comprehensive information about Algebra, Geometry, and Topology. The editors have built Issues in Algebra, Geometry, and Topology: 2011 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about Algebra, Geometry, and Topology in this eBook to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Issues in Algebra, Geometry, and Topology: 2011 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.
Author: Michael Aschbacher
Publisher: American Mathematical Soc.
ISBN: 1470456656
Category : Education
Languages : en
Pages : 444
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Book Description
Let p p be a prime and S S a finite p p-group. A p p-fusion system on S S is a category whose objects are the subgroups of S and whose morphisms are certain injective group homomorphisms. Fusion systems are of interest in modular representation theory, algebraic topology, and local finite group theory. The book provides a characterization of the 2-fusion systems of the groups of Lie type and odd characteristic, a result analogous to the Classical Involution Theorem for groups. The theorem is the most difficult step in a two-part program. The first part of the program aims to determine a large subclass of the class of simple 2-fusion systems, while part two seeks to use the result on fusion systems to simplify the proof of the theorem classifying the finite simple groups.
Author: Lluis Puig
Publisher: Birkhäuser
ISBN: 3034886934
Category : Mathematics
Languages : en
Pages : 256
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Book Description
Brauer had already introduced the defect of a block and opened the way towards a classification by solving all the problems in defects zero and one, and by providing some evidence for the finiteness of the set of blocks with a given defect. In 1959 he discovered the defect group, and in 1964 Dade determined the blocks with cyclic defect groups. In 1978 Alperin and Broué discovered the Brauer category, and Broué and the author determined the blocks having a nilpotent Brauer category. In 1979, the author discovered the source algebra which determines all the other current invariants, representing faithfully the block – and found its structure in the nilpotent blocks. Recently, the discovery by Rickard that all blocks with the same cyclic defect group and the same Brauer category have the same homotopic category focussed great interest on the new, loose relationship between blocks called Rickard equivalence. This book describes the source algebra of a block from the source algebra of a Rickard equivalent block and the source of the Rickard equivalence.
Author: Michael Aschbacher
Publisher: American Mathematical Soc.
ISBN: 0821853031
Category : Mathematics
Languages : en
Pages : 122
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Book Description
Here, the author seeks to build a local theory of fusion systems, analogous to the local theory of finite groups, involving normal subsystems and factor systems.
