Introduction to Representation Theory: (Student Mathematical Library)

Very roughly speaking, representation theory studies symmetry in linear spaces. It is a beautiful mathematical subject which has many applications, ranging from number theory and combinatorics to geometry, probability theory, quantum mechanics, and quantum field theory. The goal of this book is to give a ``holistic'' introduction to representation theory, presenting it as a unified subject which studies representations of associative algebras and treating the representation theories of groups, Lie algebras, and quivers as special cases. Using this approach, the book covers a number of standard topics in the representation theories of these structures. Theoretical material in the book is supplemented by many problems and exercises which touch upon a lot of additional topics; the more difficult exercises are provided with hints. The book is designed as a textbook for advanced undergraduate and beginning graduate students. It should be accessible to students with a strong background in linear algebra and a basic knowledge of abstract algebra.

Table of Contents:
Introduction Basic notions of representation theory General results of representation theory Representations of finite groups: Basic results Representations of finite groups: Further results Quiver representations Introduction to categories Homological algebra Structure of finite dimensional algebras References for historical interludes Bibliography Index

About the Author :
Pavel Etingof, Massachusetts Institute of Technology, Cambridge, MA, USA Oleg Golberg, Sebastian Hensel: Universität Bonn, Bonn, Germany Tiankai Liu, Massachusetts Institute of Technology, Cambridge, MA, USA Alex Schwendner, Two Sigma Investments, New York, NY, USA Dmitry Vaintrob, Harvard University, Cambridge, MA, USA Elena Yudovina, University of Cambridge, Cambridge, United Kingdom with historical interludes by Slava Gerovitch, Massachusetts Institute of Technology, Cambridge, MA, USA

Review :
This charming book ... the material in the book is quite modern, the unifying theme being the representation theory of associative algebras, and the presentation is very accessible. ...It is a truly wonderful achievement. The book is well-written, sportingly paced, and brims with mathematical elegance: the prose is clear and tight and the proofs are compact and pretty." - MAA Reviews "The book gives a concise introduction to various aspects of representation theory. It is an interesting addition to the existing literature on the subject." - Mathematical Reviews "Add to this the sets of problems included in the book, replete with occasional hints and estimates of the degree of difficulty, as well as the wonderful 'Historical Interludes' by Slava Gerovitch, and the result is a fantastic little book. I think it is bound to become the way to get into this subject 'holistically.'" - MAA Reviews