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Author : Dharam Chand Khatri
Publisher :
ISBN 13 :
Total Pages : 118 pages
Book Rating : 4.3/5 (129 download)
Download or read book Relative Projectivity and Radicals in Modular Group Algebras written by Dharam Chand Khatri and published by . This book was released on 1972 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : G. Karpilovsky
Publisher : Elsevier
ISBN 13 : 0080872468
Total Pages : 543 pages
Book Rating : 4.0/5 (88 download)
Download or read book The Jacobson Radical of Group Algebras written by G. Karpilovsky and published by Elsevier. This book was released on 1987-04-01 with total page 543 pages. Available in PDF, EPUB and Kindle. Book excerpt: Let G be a finite group and let F be a field. It is well known that linear representations of G over F can be interpreted as modules over the group algebra FG. Thus the investigation of ring-theoretic structure of the Jacobson radical J(FG) of FG is of fundamental importance. During the last two decades the subject has been pursued by a number of researchers and many interesting results have been obtained. This volume examines these results.The main body of the theory is presented, giving the central ideas, the basic results and the fundamental methods. It is assumed that the reader has had the equivalent of a standard first-year graduate algebra course, thus familiarity with basic ring-theoretic and group-theoretic concepts and an understanding of elementary properties of modules, tensor products and fields. A chapter on algebraic preliminaries is included, providing a survey of topics needed later in the book. There is a fairly large bibliography of works which are either directly relevant to the text or offer supplementary material of interest.
Author : W. Feit
Publisher : Elsevier
ISBN 13 : 0080960138
Total Pages : 517 pages
Book Rating : 4.0/5 (89 download)
Download or read book The Representation Theory of Finite Groups written by W. Feit and published by Elsevier. This book was released on 1982-05-01 with total page 517 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Representation Theory of Finite Groups
Author : P. Landrock
Publisher : Cambridge University Press
ISBN 13 : 0521274877
Total Pages : 287 pages
Book Rating : 4.5/5 (212 download)
Download or read book Finite Group Algebras and Their Modules written by P. Landrock and published by Cambridge University Press. This book was released on 1983-12-29 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Gregory Karpilovsky
Publisher : Elsevier
ISBN 13 : 1483295109
Total Pages : 973 pages
Book Rating : 4.4/5 (832 download)
Download or read book Group Representations written by Gregory Karpilovsky and published by Elsevier. This book was released on 2016-06-06 with total page 973 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is divided into three parts. Part I provides the foundations of the theory of modular representations. Special attention is drawn to the Brauer-Swan theory and the theory of Brauer characters. A detailed investigation of quadratic, symplectic and symmetric modules is also provided. Part II is devoted entirely to the Green theory: vertices and sources, the Green correspondence, the Green ring, etc. In Part III, permutation modules are investigated with an emphasis on the study of p-permutation modules and Burnside rings. The material is developed with sufficient attention to detail so that it can easily be read by the novice, although its chief appeal will be to specialists. A number of the results presented in this volume have almost certainly never been published before.
Author : G. Karpilovsky
Publisher : Elsevier
ISBN 13 : 0080872727
Total Pages : 533 pages
Book Rating : 4.0/5 (88 download)
Download or read book Induced Modules over Group Algebras written by G. Karpilovsky and published by Elsevier. This book was released on 1990-03-01 with total page 533 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Gloria Grace Potter
Publisher :
ISBN 13 :
Total Pages : 122 pages
Book Rating : 4.3/5 (129 download)
Download or read book On H-projective FG-modules and the Complete Reducibility of Induced FH-modules written by Gloria Grace Potter and published by . This book was released on 1975 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Jon F. Carlson
Publisher : Birkhäuser
ISBN 13 : 303489189X
Total Pages : 100 pages
Book Rating : 4.0/5 (348 download)
Download or read book Modules and Group Algebras written by Jon F. Carlson and published by Birkhäuser. This book was released on 2012-12-06 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : D. Benson
Publisher : Springer
ISBN 13 : 3540389407
Total Pages : 246 pages
Book Rating : 4.5/5 (43 download)
Download or read book Modular Representation Theory written by D. Benson and published by Springer. This book was released on 2008-07-22 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: This reprint of a 1983 Yale graduate course makes results in modular representation theory accessible to an audience ranging from second-year graduate students to established mathematicians. Following a review of background material, the lectures examine three closely connected topics in modular representation theory of finite groups: representations rings; almost split sequences and the Auslander-Reiten quiver; and complexity and cohomology varieties, which has become a major theme in representation theory.
Author : G. Karpilovsky
Publisher : Elsevier
ISBN 13 : 0080872670
Total Pages : 375 pages
Book Rating : 4.0/5 (88 download)
Download or read book Clifford Theory for Group Representations written by G. Karpilovsky and published by Elsevier. This book was released on 1989-05-01 with total page 375 pages. Available in PDF, EPUB and Kindle. Book excerpt: Let N be a normal subgroup of a finite group G and let F be a field. An important method for constructing irreducible FG-modules consists of the application (perhaps repeated) of three basic operations: (i) restriction to FN. (ii) extension from FN. (iii) induction from FN. This is the `Clifford Theory' developed by Clifford in 1937. In the past twenty years, the theory has enjoyed a period of vigorous development. The foundations have been strengthened and reorganized from new points of view, especially from the viewpoint of graded rings and crossed products.The purpose of this monograph is to tie together various threads of the development in order to give a comprehensive picture of the current state of the subject. It is assumed that the reader has had the equivalent of a standard first-year graduate algebra course, i.e. familiarity with basic ring-theoretic, number-theoretic and group-theoretic concepts, and an understanding of elementary properties of modules, tensor products and fields.
Author : Charles W. Curtis
Publisher : American Mathematical Soc.
ISBN 13 : 0821840665
Total Pages : 714 pages
Book Rating : 4.8/5 (218 download)
Download or read book Representation Theory of Finite Groups and Associative Algebras written by Charles W. Curtis and published by American Mathematical Soc.. This book was released on 2006 with total page 714 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides an introduction to various aspects of the representation theory of finite groups. This book covers such topics as general non-commutative algebras, Frobenius algebras, representations over non-algebraically closed fields and fields of non-zero characteristic, and integral representations.
Author : Markus Linckelmann
Publisher : Cambridge University Press
ISBN 13 : 1108425909
Total Pages : 523 pages
Book Rating : 4.1/5 (84 download)
Download or read book The Block Theory of Finite Group Algebras written by Markus Linckelmann and published by Cambridge University Press. This book was released on 2018 with total page 523 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Peter Webb
Publisher : Cambridge University Press
ISBN 13 : 1107162394
Total Pages : 339 pages
Book Rating : 4.1/5 (71 download)
Download or read book A Course in Finite Group Representation Theory written by Peter Webb and published by Cambridge University Press. This book was released on 2016-08-19 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Publisher : Springer Science & Business Media
ISBN 13 : 9401512884
Total Pages : 595 pages
Book Rating : 4.4/5 (15 download)
Download or read book Encyclopaedia of Mathematics written by Michiel Hazewinkel and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 595 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first Supplementary volume to Kluwer's highly acclaimed Encyclopaedia of Mathematics. This additional volume contains nearly 600 new entries written by experts and covers developments and topics not included in the already published 10-volume set. These entries have been arranged alphabetically throughout. A detailed index is included in the book. This Supplementary volume enhances the existing 10-volume set. Together, these eleven volumes represent the most authoritative, comprehensive up-to-date Encyclopaedia of Mathematics available.
Author : David J. Benson
Publisher : American Mathematical Society
ISBN 13 : 1470470292
Total Pages : 130 pages
Book Rating : 4.4/5 (74 download)
Download or read book Modular Representation Theory and Commutative Banach Algebras written by David J. Benson and published by American Mathematical Society. This book was released on 2024-07-25 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.
Author : Gregory Karpilovsky
Publisher : Longman Scientific and Technical
ISBN 13 :
Total Pages : 454 pages
Book Rating : 4.3/5 (91 download)
Download or read book Structure of Blocks of Group Algebras written by Gregory Karpilovsky and published by Longman Scientific and Technical. This book was released on 1987 with total page 454 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Markus Linckelmann
Publisher : Cambridge University Press
ISBN 13 : 1108562582
Total Pages : 523 pages
Book Rating : 4.1/5 (85 download)
Download or read book The Block Theory of Finite Group Algebras: Volume 2 written by Markus Linckelmann and published by Cambridge University Press. This book was released on 2018-05-24 with total page 523 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
