Modules and Group Algebras PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Modules and Group Algebras PDF full book. Access full book title Modules and Group Algebras by Jon F. Carlson. Download full books in PDF and EPUB format.
Author: Jon F. Carlson
Publisher: Birkhäuser
ISBN: 303489189X
Category : Mathematics
Languages : en
Pages : 100
Get Book
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: Jon F. Carlson
Publisher: Birkhäuser
ISBN: 303489189X
Category : Mathematics
Languages : en
Pages : 100
Get Book
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: Alberto Facchini
Publisher: CRC Press
ISBN: 9780824750817
Category : Mathematics
Languages : en
Pages : 530
Get Book
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: Michiel Hazewinkel
Publisher: CRC Press
ISBN: 1482245051
Category : Mathematics
Languages : en
Pages : 388
Get Book
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 century. This volume is a continuation and an in-depth study, stressing the non-commutative nature of the first two volumes of Algebras, Rings and Modules by M. Hazewinkel, N. Gubareni, and V. V. Kirichenko. It is largely independent of the other volumes. The relevant constructions and results from earlier volumes have been presented in this volume.
Author: Jon F Carlson
Publisher:
ISBN: 9783034891905
Category : Group algebras
Languages : en
Pages : 108
Get Book
Book Description
Author: Peter Webb
Publisher: Cambridge University Press
ISBN: 1107162394
Category : Mathematics
Languages : en
Pages : 339
Get Book
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: J. F. Carlson
Publisher: Birkhauser
ISBN: 9780817653897
Category : Group algebras
Languages : en
Pages : 91
Get Book
Book Description
"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
ISBN: 0521274877
Category : Mathematics
Languages : en
Pages : 287
Get Book
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: G. Karpilovsky
Publisher: Elsevier
ISBN: 9780080872728
Category : Mathematics
Languages : en
Pages : 519
Get Book
Book Description
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: Gregory Karpilovsky
Publisher:
ISBN: 9780444558343
Category :
Languages : en
Pages : 520
Get Book
Book Description
Author: Robert Wisbauer
Publisher: CRC Press
ISBN: 9780582289819
Category : Mathematics
Languages : en
Pages : 384
Get Book
Book Description
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.
