Modular Representation Theory Of Finite And P Adic Groups
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Author | : Wee Teck Gan |
Publisher | : World Scientific |
Total Pages | : 277 |
Release | : 2015-02-13 |
Genre | : Mathematics |
ISBN | : 9814651826 |
This volume is an outgrowth of the program Modular Representation Theory of Finite and p-Adic Groups held at the Institute for Mathematical Sciences at National University of Singapore during the period of 1-26 April 2013. It contains research works in the areas of modular representation theory of p-adic groups and finite groups and their related algebras. The aim of this volume is to provide a bridge — where interactions are rare between researchers from these two areas — by highlighting the latest developments, suggesting potential new research problems, and promoting new collaborations.It is perhaps one of the few volumes, if not only, which treats such a juxtaposition of diverse topics, emphasizing their common core at the heart of Lie theory.
Author | : Martin Burrow |
Publisher | : Academic Press |
Total Pages | : 196 |
Release | : 2014-05-10 |
Genre | : Mathematics |
ISBN | : 1483258211 |
Representation Theory of Finite Groups is a five chapter text that covers the standard material of representation theory. This book starts with an overview of the basic concepts of the subject, including group characters, representation modules, and the rectangular representation. The succeeding chapters describe the features of representation theory of rings with identity and finite groups. These topics are followed by a discussion of some of the application of the theory of characters, along with some classical theorems. The last chapter deals with the construction of irreducible representations of groups. This book will be of great value to graduate students who wish to acquire some knowledge of representation theory.
Author | : Peter Schneider |
Publisher | : Springer Science & Business Media |
Total Pages | : 183 |
Release | : 2012-11-27 |
Genre | : Mathematics |
ISBN | : 1447148320 |
Representation theory studies maps from groups into the general linear group of a finite-dimensional vector space. For finite groups the theory comes in two distinct flavours. In the 'semisimple case' (for example over the field of complex numbers) one can use character theory to completely understand the representations. This by far is not sufficient when the characteristic of the field divides the order of the group. Modular Representation Theory of finite Groups comprises this second situation. Many additional tools are needed for this case. To mention some, there is the systematic use of Grothendieck groups leading to the Cartan matrix and the decomposition matrix of the group as well as Green's direct analysis of indecomposable representations. There is also the strategy of writing the category of all representations as the direct product of certain subcategories, the so-called 'blocks' of the group. Brauer's work then establishes correspondences between the blocks of the original group and blocks of certain subgroups the philosophy being that one is thereby reduced to a simpler situation. In particular, one can measure how nonsemisimple a category a block is by the size and structure of its so-called 'defect group'. All these concepts are made explicit for the example of the special linear group of two-by-two matrices over a finite prime field. Although the presentation is strongly biased towards the module theoretic point of view an attempt is made to strike a certain balance by also showing the reader the group theoretic approach. In particular, in the case of defect groups a detailed proof of the equivalence of the two approaches is given. This book aims to familiarize students at the masters level with the basic results, tools, and techniques of a beautiful and important algebraic theory. Some basic algebra together with the semisimple case are assumed to be known, although all facts to be used are restated (without proofs) in the text. Otherwise the book is entirely self-contained.
Author | : Charles W. Curtis |
Publisher | : Wiley-Interscience |
Total Pages | : 984 |
Release | : 1981 |
Genre | : Mathematics |
ISBN | : |
Revised and expanded, this second volume presents a modern treatment of finite groups and orders. It covers classical, modular and integral representation theory and contains many important new results. Beginning with an introductory review of ring theory, algebraic number theory, and homological algebra, the book then moves on to other topics such as modular representations and integral representation theory. Also covered are class groups and Picard groups, the theory of blocks, rationality questions, indecomposable modules and more.
Author | : Peter Webb |
Publisher | : Cambridge University Press |
Total Pages | : 339 |
Release | : 2016-08-19 |
Genre | : Mathematics |
ISBN | : 1107162394 |
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 | : Larry L. Dornhoff |
Publisher | : |
Total Pages | : 280 |
Release | : 1971 |
Genre | : Mathematics |
ISBN | : |
Author | : D. Benson |
Publisher | : Springer Science & Business Media |
Total Pages | : 246 |
Release | : 1984 |
Genre | : Mathematics |
ISBN | : 3540133895 |
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 | : |
Publisher | : Academic Press |
Total Pages | : 259 |
Release | : 1977-03-14 |
Genre | : Mathematics |
ISBN | : 0080873898 |
Modular Representations of Finite Groups
Author | : I. Reiner |
Publisher | : Springer |
Total Pages | : 284 |
Release | : 2006-11-15 |
Genre | : Mathematics |
ISBN | : 3540350071 |
Author | : Peter Schneider |
Publisher | : Cambridge University Press |
Total Pages | : 157 |
Release | : 2017-04-20 |
Genre | : Mathematics |
ISBN | : 110718858X |
A detailed and self-contained introduction to a key part of local number theory, ideal for graduate students and researchers.