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.
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.
Download or read book Rings Modules Algebras and Abelian Groups written by Alberto Facchini and published by CRC Press. This book was released on 2018-09-18 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 algebraic structures, and provides more than 600 current references and 570 display equations for further exploration of the topic. It provides stimulating discussions from world-renowned names including Laszlo Fuchs, Robert Gilmer, Saharon Shelah, Daniel Simson, and Richard Swan to celebrate 40 years of study on cumulative rings. Describing emerging theories
Download or read book Representations of Finite Groups written by Hirosi Nagao and published by Elsevier. This book was released on 2014-05-10 with total page 443 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Representations of Algebraic Groups written by Jens Carsten Jantzen and published by American Mathematical Soc.. This book was released on 2003 with total page 594 pages. Available in PDF, EPUB and Kindle. Book excerpt: Gives an introduction to the general theory of representations of algebraic group schemes. This title deals with representation theory of reductive algebraic groups and includes topics such as the description of simple modules, vanishing theorems, Borel-Bott-Weil theorem and Weyl's character formula, and Schubert schemes and lne bundles on them.
Download or read book Algebras and Representation Theory written by Karin Erdmann and published by Springer. This book was released on 2018-09-07 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: This carefully written textbook provides an accessible introduction to the representation theory of algebras, including representations of quivers. The book starts with basic topics on algebras and modules, covering fundamental results such as the Jordan-Hölder theorem on composition series, the Artin-Wedderburn theorem on the structure of semisimple algebras and the Krull-Schmidt theorem on indecomposable modules. The authors then go on to study representations of quivers in detail, leading to a complete proof of Gabriel's celebrated theorem characterizing the representation type of quivers in terms of Dynkin diagrams. Requiring only introductory courses on linear algebra and groups, rings and fields, this textbook is aimed at undergraduate students. With numerous examples illustrating abstract concepts, and including more than 200 exercises (with solutions to about a third of them), the book provides an example-driven introduction suitable for self-study and use alongside lecture courses.
Download or read book Idempotent Matrices over Complex Group Algebras written by Ioannis Emmanouil and published by Springer Science & Business Media. This book was released on 2005-12-19 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of idempotent matrices with entries in complex group algebras has recently experienced a revival, in view of its close relationship with deep geometric problems and conjectures. The relevant questions studied in this book for general groups are motivated by specific examples. A variety of techniques is employed from commutative algebra, homological algebra and functional analysis.The book can serve as an introduction to this lively research area. The pace is suitable for independent study and the level of the presentation not very demanding. The exercises at the end of each chapter form an essential part of the book.
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.
Download or read book Group and Semigroup Rings written by G. Karpilovsky and published by Elsevier. This book was released on 2011-09-22 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: A broad range of topics is covered here, including commutative monoid rings, the Jacobson radical of semigroup rings, blocks of modular group algebras, nilpotency index of the radical of group algebras, the isomorphism problem for group rings, inverse semigroup algebras and the Picard group of an abelian group ring. The survey lectures provide an up-to-date account of the current state of the subject and form a comprehensive introduction for intending researchers.
Download or read book Groups St Andrews 1997 in Bath Volume 2 written by C. M. Campbell and published by Cambridge University Press. This book was released on 1999-02-18 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: This two-volume book contains selected papers from the international conference "Groups St. Andrews 1997 in Bath". The articles are arranged in roughly alphabetical order and cover a wide spectrum of modern group theory. There are articles based on lecture courses given by five main speakers together with refereed survey and research articles contributed by other conference participants. Proceedings of earlier "Groups St. Andrews" conferences have had a major impact on the development of group theory and these volumes should be equally important.
Download or read book Group Representations written by and published by Elsevier. This book was released on 1994-02-18 with total page 925 pages. Available in PDF, EPUB and Kindle. Book excerpt: This third volume can be roughly divided into two parts. The first part is devoted to the investigation of various properties of projective characters. Special attention is drawn to spin representations and their character tables and to various correspondences for projective characters. Among other topics, projective Schur index and projective representations of abelian groups are covered. The last topic is investigated by introducing a symplectic geometry on finite abelian groups.The second part is devoted to Clifford theory for graded algebras and its application to the corresponding theory for group algebras. The volume ends with a detailed investigation of the Schur index for ordinary representations. A prominant role is played in the discussion by Brauer groups together with cyclotomic algebras and cyclic algebras.
Download or read book Structure Theorems of Unit Groups written by Eric Jespers and published by Walter de Gruyter GmbH & Co KG. This book was released on 2015-11-13 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: This two-volume graduate textbook gives a comprehensive, state-of-the-art account of describing large subgroups of the unit group of the integral group ring of a finite group and, more generally, of the unit group of an order in a finite dimensional semisimple rational algebra. Since the book is addressed to graduate students as well as young researchers, all required background on these diverse areas, both old and new, is included. Supporting problems illustrate the results and complete some of the proofs. Volume 1 contains all the details on describing generic constructions of units and the subgroup they generate. Volume 2 mainly is about structure theorems and geometric methods. Without being encyclopaedic, all main results and techniques used to achieve these results are included. Basic courses in group theory, ring theory and field theory are assumed as background.
Download or read book Group Representations Volume 1 Part B written by and published by Elsevier. This book was released on 1992-07-09 with total page 669 pages. Available in PDF, EPUB and Kindle. Book excerpt: Group Representations Volume 1 Part B
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.
Download or read book Groups Algebras and Applications written by César Polcino Milies and published by American Mathematical Soc.. This book was released on 2011 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains the proceedings of the XVIII Latin American Algebra Colloquium, held from August 3-8, 2009, in Sao Paulo, Brazil. It includes research articles as well as up-to-date surveys covering several directions of current research in algebra, such as Asymptotic Codimension Growth, Hopf Algebras, Structure Theory of both Associative and Non-Associative Algebras, Partial Actions of Groups on Rings, and contributions to Coding Theory.
Download or read book Lie Algebras and Their Representations written by Seok-Jin Kang and published by American Mathematical Soc.. This book was released on 1996 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the past 30 years, exciting developments in diverse areas of the theory of Lie algebras and their representations have been observed. The symposium covered topics such as Lie algebras and combinatorics, crystal bases for quantum groups, quantum groups and solvable lattice models, and modular and infinite-dimensional Lie algebras. In this volume, readers will find several excellent expository articles and research papers containing many significant new results in this area.
Download or read book Representations and Cohomology Volume 2 Cohomology of Groups and Modules written by D. J. Benson and published by Cambridge University Press. This book was released on 1991-08-22 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: A further introduction to modern developments in the representation theory of finite groups and associative algebras.
