The Ring Of Representation

This book asks how we may undertake to represent representation.

A study of representations of rings over skew fields.

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.

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.

The circus has been both one of the most influential forms of international popular entertainment and yet at the same time remains almost entirely absent from academic studies of popular theatrical forms. This book offers readers an introduction to the cultural history of the circus and gives an account of the dominant characteristics of the circus's aesthetic practices and relates these to the sometimes precarious developments, changes and variations in its economic organization, architecture and social status. The book goes on to outline the particular challenges that this essentially live, dangerous and body-centred form presents to literary and film representation and does so through the particular examples of works by Charles Dickens, Federico Fellini and Wim Wenders. This wide-ranging and accessible book offers ways of thinking about the meaning and significance of the circus as a specifically modern form of art and entertainment.

This volume is dedicated to the memory of the Soviet mathematician S. D. Berman (1922-1987). Berman's work - for the most part in representation theory, group rings, and coding theory - is discussed here in a number of review articles. Among the topics covered are Berman's achievements in coding theory, including his pioneering work on abelian codes and his results on the theory of threshold functions. Also discussed are his contributions to the representation theory of groups over fields, his work on integral representations of groups, his accomplishments in infinite abelian group rings, and his fundamental results on units in integral group rings. In addition, there are 22 research articles written by an international group of researchers in areas of Berman's major interest.

The papers in this volume contain results in active research areas in the theory of rings and modules, including non commutative and commutative ring theory, module theory, representation theory, and coding theory.