Introduction to Representation Theory
( Student Mathematical Library )
Publication series ：Student Mathematical Library
Author： Pavel Etingof;Oleg Golberg;Sebastian Hensel
Publisher： American Mathematical Society
Publication year： 2011
E-ISBN: 9781470412227
P-ISBN(Paperback): 9780821853511
Subject： O15 algebra, number theory, combinatorial theory
Keyword： Algebra and Algebraic Geometry
Language： ENG
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Introduction to Representation Theory
Description
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.
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