Overview

Representation theory investigates the different ways in which a given algebraic object--such as a group or a Lie algebra--can act on a vector space. Besides being a subject of great intrinsic beauty, the theory enjoys the additional benefit of having applications in myriad contexts outside pure mathematics, including quantum field theory and the study of molecules in chemistry. Adopting a panoramic viewpoint, this book offers an introduction to four different flavors of representation theory: representations of algebras, groups, Lie algebras, and Hopf algebras. A separate part of the book is devoted to each of these areas and they are all treated in sufficient depth to enable and hopefully entice the reader to pursue research in representation theory. The book is intended as a textbook for a course on representation theory, which could immediately follow the standard graduate abstract algebra course, and for subsequent more advanced reading courses. Therefore, more than 350 exercises at various levels of difficulty are included. The broad range of topics covered will also make the text a valuable reference for researchers in algebra and related areas and a source for graduate and postgraduate students wishing to learn more about representation theory by self-study.

Full Product Details

Author:   Martin Lorenz
Publisher:   American Mathematical Society
Imprint:   American Mathematical Society
Weight:   1.355kg
ISBN:  

9781470436803

ISBN 10:   1470436809
Pages:   654
Publication Date:   30 October 2018
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

Algebras: Representations of algebras Further topics on algebras Groups: Groups and group algebras Symmetric groups Lie algebras: Lie algebras and enveloping algebras Semisimple Lie algebras Root systems Representations of semisimple Lie algebras Hopf algebras: Coalgebras, bialgebras, and Hopf algebras Representations and actions Affine algebraic groups Finite-dimensional Hopf algebras Appendices: The language of categories and functors Background from linear algebra Some commutative algebra The Diamond Lemma The symmetric ring of quotients Bibliography Subject index Index of names Notation.

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Martin Lorenz, Temple University, Philadelphia, PA.

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