Modules And Group Algebras

Author : Jon F. Carlson
Publisher : Birkhäuser
Page : 100 pages
File Size : 42,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034891899

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Modules and Group Algebras by Jon F. Carlson Pdf

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 : Jon F Carlson
Publisher : Unknown
Page : 108 pages
File Size : 50,8 Mb
Release : 1996-02-29
Category : Group algebras
ISBN : 3034891903

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Modules and Group Algebras by Jon F Carlson Pdf

Author : J. F. Carlson,Ruedi Suter
Publisher : Birkhauser
Page : 91 pages
File Size : 55,8 Mb
Release : 1996-01-01
Category : Group algebras
ISBN : 0817653899

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Modules and Group Algebras by J. F. Carlson,Ruedi Suter Pdf

"These notes grew out of a Nachdiplom course given at the ETH Zurich in the summer semester of 1995. They aim at the development of some of the basics of the interaction of homological algebra, or more specifically the cohomology of groups, and modular representation theory." "The book presents an entirely new approach to the subject based on the recent development in this field. Basically the shift has been towards a much more categorical view of representation theory, and an expansion of the viewpoint to include infinitely generated modules as well as the finitely generated ones. Some of the constructions in the category of all modules have had new and original applications for the category of finitely generated modules." "This introduction to a fresh view of the module theory for finite groups is of interest to students and researchers in homotopy theory and group actions as well as the representation theory of finite groups." --Book Jacket.

Author : P. Landrock
Publisher : Cambridge University Press
Page : 287 pages
File Size : 46,6 Mb
Release : 1983-12-29
Category : Mathematics
ISBN : 9780521274876

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Finite Group Algebras and Their Modules by P. Landrock Pdf

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 : Alberto Facchini,Evan Houston,Luigi Salce
Publisher : CRC Press
Page : 530 pages
File Size : 44,9 Mb
Release : 2020-02-10
Category : Mathematics
ISBN : 0824750810

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Rings, Modules, Algebras, and Abelian Groups by Alberto Facchini,Evan Houston,Luigi Salce Pdf

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 : Robert Wisbauer
Publisher : CRC Press
Page : 384 pages
File Size : 44,9 Mb
Release : 1996-05-15
Category : Mathematics
ISBN : 0582289815

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Modules and Algebras by Robert Wisbauer Pdf

Module theory over commutative asociative rings is usually extended to noncommutative associative rings by introducing the category of left (or right) modules. An alternative to this procedure is suggested by considering bimodules. A refined module theory for associative rings is used to investigate the bimodule structure of arbitary algebras and group actions on these algebras.

Author : G. Karpilovsky
Publisher : Elsevier
Page : 519 pages
File Size : 40,5 Mb
Release : 1990-03-01
Category : Mathematics
ISBN : 0080872727

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Induced Modules over Group Algebras by G. Karpilovsky Pdf

In 1898 Frobenius discovered a construction which, in present terminology, associates with every module of a subgroup the induced module of a group. This construction proved to be of fundamental importance and is one of the basic tools in the entire theory of group representations. This monograph is designed for research mathematicians and advanced graduate students and gives a picture of the general theory of induced modules as it exists at present. Much of the material has until now been available only in research articles. The approach is not intended to be encyclopedic, rather each topic is considered in sufficient depth that the reader may obtain a clear idea of the major results in the area. After establishing algebraic preliminaries, the general facts about induced modules are provided, as well as some of their formal properties, annihilators and applications. The remaining chapters include detailed information on the process of induction from normal subgroups, projective summands of induced modules, some basic results of the Green theory with refinements and extensions, simple induction and restriction pairs and permutation modules. The final chapter is based exclusively on the work of Weiss, presenting a number of applications to the isomorphism problem for group rings.

Author : Peter Webb
Publisher : Cambridge University Press
Page : 339 pages
File Size : 45,5 Mb
Release : 2016-08-19
Category : Mathematics
ISBN : 9781107162396

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A Course in Finite Group Representation Theory by Peter Webb Pdf

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 : Michiel Hazewinkel,Nadiya Gubareni,V.V. Kirichenko
Publisher : Springer Science & Business Media
Page : 393 pages
File Size : 48,5 Mb
Release : 2006-01-18
Category : Mathematics
ISBN : 9781402026911

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Algebras, Rings and Modules by Michiel Hazewinkel,Nadiya Gubareni,V.V. Kirichenko Pdf

Accosiative rings and algebras are very interesting algebraic structures. In a strict sense, the theory of algebras (in particular, noncommutative algebras) originated fromasingleexample,namelythequaternions,createdbySirWilliamR.Hamilton in1843. Thiswasthe?rstexampleofanoncommutative”numbersystem”. During thenextfortyyearsmathematiciansintroducedotherexamplesofnoncommutative algebras, began to bring some order into them and to single out certain types of algebras for special attention. Thus, low-dimensional algebras, division algebras, and commutative algebras, were classi?ed and characterized. The ?rst complete results in the structure theory of associative algebras over the real and complex ?elds were obtained by T.Molien, E.Cartan and G.Frobenius. Modern ring theory began when J.H.Wedderburn proved his celebrated cl- si?cation theorem for ?nite dimensional semisimple algebras over arbitrary ?elds. Twenty years later, E.Artin proved a structure theorem for rings satisfying both the ascending and descending chain condition which generalized Wedderburn structure theorem. The Wedderburn-Artin theorem has since become a corn- stone of noncommutative ring theory. The purpose of this book is to introduce the subject of the structure theory of associative rings. This book is addressed to a reader who wishes to learn this topic from the beginning to research level. We have tried to write a self-contained book which is intended to be a modern textbook on the structure theory of associative rings and related structures and will be accessible for independent study.

Author : Gregory Karpilovsky
Publisher : Unknown
Page : 520 pages
File Size : 49,6 Mb
Release : 1990
Category : Electronic
ISBN : 0444558349

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Induced Modules Over Group Algebras by Gregory Karpilovsky Pdf

Author : Idun Reiten,Sverre O. Smalø,Øyvind Solberg,Canadian Mathematical Society
Publisher : American Mathematical Soc.
Page : 216 pages
File Size : 52,5 Mb
Release : 1998
Category : Mathematics
ISBN : 0821808508

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Algebras and Modules I by Idun Reiten,Sverre O. Smalø,Øyvind Solberg,Canadian Mathematical Society Pdf

Surveys developments in the representation theory of finite dimensional algebras and related topics in seven papers illustrating different techniques developed over the recent years. For graduate students and researchers with a background in commutative algebra, including rings, modules, and homological algebra. Suitable as a text for an advanced graduate course. No index. Member prices are $31 for institutions and $23 for individuals, and are available to members of the Canadian Mathematical Society. Annotation copyrighted by Book News, Inc., Portland, OR

Author : Friedrich Wagemann
Publisher : Walter de Gruyter GmbH & Co KG
Page : 342 pages
File Size : 42,7 Mb
Release : 2021-10-25
Category : Mathematics
ISBN : 9783110750997

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Crossed Modules by Friedrich Wagemann Pdf

This book presents material in two parts. Part one provides an introduction to crossed modules of groups, Lie algebras and associative algebras with fully written out proofs and is suitable for graduate students interested in homological algebra. In part two, more advanced and less standard topics such as crossed modules of Hopf algebra, Lie groups, and racks are discussed as well as recent developments and research on crossed modules.

Author : Markus Linckelmann
Publisher : Cambridge University Press
Page : 523 pages
File Size : 52,7 Mb
Release : 2018-05-24
Category : Mathematics
ISBN : 9781108425902

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The Block Theory of Finite Group Algebras by Markus Linckelmann Pdf

A comprehensive treatment of block theory, emphasising cornerstones of the area which have not appeared in any book before.

Author : M.R. Adhikari,A. Adhikari
Publisher : Universities Press
Page : 336 pages
File Size : 44,8 Mb
Release : 2003
Category : Commutative rings
ISBN : 8173714290

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Groups, Rings And Modules With Applications by M.R. Adhikari,A. Adhikari Pdf

Author : Peter Landrock
Publisher : Unknown
Page : 286 pages
File Size : 43,6 Mb
Release : 2014-05-14
Category : MATHEMATICS
ISBN : 1107087279

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Finite Group Alegebras and Their Modules by Peter Landrock Pdf

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.