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Author: Peter Landrock
Publisher:
ISBN: 9781107087279
Category : MATHEMATICS
Languages : en
Pages : 286
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Book Description
Originally published in 1983, the principal object of this book is to discuss in detail the structure of finite group rings over fields of characteristic, p, P-adic rings and, in some cases, just principal ideal domains, as well as modules of such group rings. The approach does not emphasize any particular point of view, but aims to present a smooth proof in each case to provide the reader with maximum insight. However, the trace map and all its properties have been used extensively. This generalizes a number of classical results at no extra cost and also has the advantage that no assumption on the field is required. Finally, it should be mentioned that much attention is paid to the methods of homological algebra and cohomology of groups as well as connections between characteristic 0 and characteristic p.
Author: Peter Landrock
Publisher:
ISBN: 9781107087279
Category : MATHEMATICS
Languages : en
Pages : 286
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Book Description
Originally published in 1983, the principal object of this book is to discuss in detail the structure of finite group rings over fields of characteristic, p, P-adic rings and, in some cases, just principal ideal domains, as well as modules of such group rings. The approach does not emphasize any particular point of view, but aims to present a smooth proof in each case to provide the reader with maximum insight. However, the trace map and all its properties have been used extensively. This generalizes a number of classical results at no extra cost and also has the advantage that no assumption on the field is required. Finally, it should be mentioned that much attention is paid to the methods of homological algebra and cohomology of groups as well as connections between characteristic 0 and characteristic p.
Author: P. Landrock
Publisher: Cambridge University Press
ISBN: 0521274877
Category : Mathematics
Languages : en
Pages : 287
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Book Description
This book is concerned with the structure of group algebras of finite groups over fields of characteristic [lowercase italic]p dividing the order of the group, or closely related rings such as rings of algebraic integers and in particular their [lowercase italic]p-adic completions, as well as modules and homomorphisms between them, or such group algebras. Our principal aim has been to present some of the more recent ideas which have enriched and improved this theory. This text is not restricted to particular methods, be they ring theoretic or character theoretic, while presenting approaches or proofs which are distinguished by being fast, elegant, illuminating, with potential for further advancement, or all of these at the same time. This text hopes to attract non-specialists, perhaps algebraic topologists and group theorists who might use the tools of modular representations more frequently.
Author: Hirosi Nagao
Publisher: Elsevier
ISBN: 1483269930
Category : Mathematics
Languages : en
Pages : 443
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Book Description
Representations of Finite Groups provides an account of the fundamentals of ordinary and modular representations. This book discusses the fundamental theory of complex representations of finite groups. Organized into five chapters, this book begins with an overview of the basic facts about rings and modules. This text then provides the theory of algebras, including theories of simple algebras, Frobenius algebras, crossed products, and Schur indices with representation-theoretic versions of them. Other chapters include a survey of the fundamental theory of modular representations, with emphasis on Brauer characters. This book discusses as well the module-theoretic representation theory due to Green and includes some topics such as Burry–Carlson's theorem and Scott modules. The final chapter deals with the fundamental results of Brauer on blocks and Fong's theory of covering, and includes some approaches to them. This book is a valuable resource for readers who are interested in the various approaches to the study of the representations of groups.
Author: Jon F. Carlson
Publisher: Birkhäuser
ISBN: 303489189X
Category : Mathematics
Languages : en
Pages : 100
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Book Description
The notes in this volume were written as a part of a Nachdiplom course that I gave at the ETH in the summer semester of 1995. The aim of my lectures was the development of some of the basics of the interaction of homological algebra, or more specifically the cohomology of groups, and modular representation theory. Every time that I had given such a course in the past fifteen years, the choice of the material and the order of presentation of the results have followed more or less the same basic pattern. Such a course began with the fundamentals of group cohomology, and then investigated the structure of cohomology rings, and their maximal ideal spectra. Then the variety of a module was defined and related to actual module structure through the rank variety. Applications followed. The standard approach was used in my University of Essen Lecture Notes [e1] in 1984. Evens [E] and Benson [B2] have written it up in much clearer detail and included it as part of their books on the subject.
Author: Markus Linckelmann
Publisher: Cambridge University Press
ISBN: 1108425909
Category : Blocks
Languages : en
Pages : 523
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Book Description
Author: Peter Webb
Publisher: Cambridge University Press
ISBN: 1107162394
Category : Mathematics
Languages : en
Pages : 339
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Book Description
This graduate-level text provides a thorough grounding in the representation theory of finite groups over fields and rings. The book provides a balanced and comprehensive account of the subject, detailing the methods needed to analyze representations that arise in many areas of mathematics. Key topics include the construction and use of character tables, the role of induction and restriction, projective and simple modules for group algebras, indecomposable representations, Brauer characters, and block theory. This classroom-tested text provides motivation through a large number of worked examples, with exercises at the end of each chapter that test the reader's knowledge, provide further examples and practice, and include results not proven in the text. Prerequisites include a graduate course in abstract algebra, and familiarity with the properties of groups, rings, field extensions, and linear algebra.
Author: Alberto Facchini
Publisher: CRC Press
ISBN: 9780824750817
Category : Mathematics
Languages : en
Pages : 530
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Book Description
Rings, Modules, Algebras, and Abelian Groups summarizes the proceedings of a recent algebraic conference held at Venice International University in Italy. Surveying the most influential developments in the field, this reference reviews the latest research on Abelian groups, algebras and their representations, module and ring theory, and topological
Author: Markus Linckelmann
Publisher: Cambridge University Press
ISBN: 1108425917
Category : Blocks
Languages : en
Pages : 527
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Book Description
This is a comprehensive introduction to the modular representation theory of finite groups, with an emphasis on block theory. The two volumes take into account classical results and concepts as well as some of the modern developments in the area. Volume 1 introduces the broader context, starting with general properties of finite group algebras over commutative rings, moving on to some basics in character theory and the structure theory of algebras over complete discrete valuation rings. In Volume 2, blocks of finite group algebras over complete p-local rings take centre stage, and many key results which have not appeared in a book before are treated in detail. In order to illustrate the wide range of techniques in block theory, the book concludes with chapters classifying the source algebras of blocks with cyclic and Klein four defect groups, and relating these classifications to the open conjectures that drive block theory.
Author: Markus Linckelmann
Publisher: Cambridge University Press
ISBN: 1108642187
Category : Mathematics
Languages : en
Pages : 528
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Book Description
This is a comprehensive introduction to the modular representation theory of finite groups, with an emphasis on block theory. The two volumes take into account classical results and concepts as well as some of the modern developments in the area. Volume 1 introduces the broader context, starting with general properties of finite group algebras over commutative rings, moving on to some basics in character theory and the structure theory of algebras over complete discrete valuation rings. In Volume 2, blocks of finite group algebras over complete p-local rings take centre stage, and many key results which have not appeared in a book before are treated in detail. In order to illustrate the wide range of techniques in block theory, the book concludes with chapters classifying the source algebras of blocks with cyclic and Klein four defect groups, and relating these classifications to the open conjectures that drive block theory.
Author: Michiel Hazewinkel
Publisher: CRC Press
ISBN: 1482245051
Category : Mathematics
Languages : en
Pages : 384
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Book Description
The theory of algebras, rings, and modules is one of the fundamental domains of modern mathematics. General algebra, more specifically non-commutative algebra, is poised for major advances in the twenty-first century (together with and in interaction with combinatorics), just as topology, analysis, and probability experienced in the twentieth centu
