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Author: Peter Webb Publisher: Cambridge University Press ISBN: 1107162394 Category : Mathematics Languages : en Pages : 339
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: Peter Webb Publisher: Cambridge University Press ISBN: 1107162394 Category : Mathematics Languages : en Pages : 339
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: 9781138401839 Category : Languages : en Pages :
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 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
Author: Jon F. Carlson Publisher: Birkhäuser ISBN: 303489189X Category : Mathematics Languages : en Pages : 100
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.
Book Description
This book gives a comprehensive treatment of the theory of G-Algebras and shows how it can be used to solve a number of problems about blocks, modules and almost split sequences. The new approach to modular representation theory of finite groups was developed mainly by Lluis Puig since the 1970s and has several characteristic features: unification of several theories (e.g. block theory and module theory) under a single concept, introduction of new invariants (e.g. source algebras and multiplicity modules) which shed new light on the whole, new point of view on some classical theorems (e.g. Brauer's second main theorem) yielding more precise results, deep structural results such as Puig's theory on nilpotent blocks.
Author: Thomas Scott Blyth Publisher: ISBN: Category : Mathematics Languages : en Pages : 376
Book Description
This textbook provides a self-contained course on the basic properties of modules and their importance in the theory of linear algebra. The first 11 chapters introduce the central results and applications of the theory of modules. Subsequent chapters deal with advanced linear algebra, including multilinear and tensor algebra, and explore such topics as the exterior product approach to the determinants of matrices, a module-theoretic approach to the structure of finitely generated Abelian groups, canonical forms, and normal transformations. Suitable for undergraduate courses, the text now includes a proof of the celebrated Wedderburn-Artin theorem which determines the structure of simple Artinian rings.
Author: William A. Adkins Publisher: Springer Science & Business Media ISBN: 9780387978390 Category : Mathematics Languages : en Pages : 548
Book Description
First year graduate algebra text. The choice of topics is guided by the underlying theme of modules as a basic unifying concept in mathematics. Beginning with standard topics in group and ring theory, the authors then develop basic module theory and its use in investigating bilinear, sesquilinear, and quadratic forms. Annotation copyrighted by Book News, Inc., Portland, OR
Author: Andrew Mathas Publisher: American Mathematical Soc. ISBN: 0821819267 Category : Mathematics Languages : en Pages : 204
Book Description
This volume presents a fully self-contained introduction to the modular representation theory of the Iwahori-Hecke algebras of the symmetric groups and of the $q$-Schur algebras. The study of these algebras was pioneered by Dipper and James in a series of landmark papers. The primary goal of the book is to classify the blocks and the simple modules of both algebras. The final chapter contains a survey of recent advances and open problems. The main results are proved by showing that the Iwahori-Hecke algebras and $q$-Schur algebras are cellular algebras (in the sense of Graham and Lehrer). This is proved by exhibiting natural bases of both algebras which are indexed by pairs of standard and semistandard tableaux respectively. Using the machinery of cellular algebras, which is developed in chapter 2, this results in a clean and elegant classification of the irreducible representations of both algebras. The block theory is approached by first proving an analogue of the Jantzen sum formula for the $q$-Schur algebras. This book is the first of its kind covering the topic. It offers a substantially simplified treatment of the original proofs. The book is a solid reference source for experts. It will also serve as a good introduction to students and beginning researchers since each chapter contains exercises and there is an appendix containing a quick development of the representation theory of algebras. A second appendix gives tables of decomposition numbers.
Author: John Dauns Publisher: Cambridge University Press ISBN: 0521462584 Category : Mathematics Languages : en Pages : 470
Book Description
This book on modern module and non-commutative ring theory is ideal for beginning graduate students. It starts at the foundations of the subject and progresses rapidly through the basic concepts to help the reader reach current research frontiers. Students will have the chance to develop proofs, solve problems, and to find interesting questions. The first half of the book is concerned with free, projective, and injective modules, tensor algebras, simple modules and primitive rings, the Jacobson radical, and subdirect products. Later in the book, more advanced topics, such as hereditary rings, categories and functors, flat modules, and purity are introduced. These later chapters will also prove a useful reference for researchers in non-commutative ring theory. Enough background material (including detailed proofs) is supplied to give the student a firm grounding in the subject.
Author: Jens Carsten Jantzen Publisher: American Mathematical Soc. ISBN: 082184377X Category : Mathematics Languages : en Pages : 594
Book Description
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.
Author: Peter Webb
Author: Peter Webb
Author: Alberto Facchini
Author: Jon F. Carlson
Author: Jacques Thévenaz
Author: Markus Linckelmann
Author: Thomas Scott Blyth
Author: William A. Adkins
Author: Andrew Mathas
Author: John Dauns
Author: Jens Carsten Jantzen