Introduction to representation theory
By: Pavel Etingof ... [et al.] ; with historical interludes by Slava Gerovitch
Series: Student mathematical library -- v. 59
Publisher: American Mathematical Society
Published: 2011
Place of publication: Providence, R.I
Language: eng
Number of pages: 228
ISBN-13: 9780821853511
Subjects: Associative rings and algebras -- Representation theory of rings and algebras -- Representation theory of rings and algebras; Group theory and generalizations -- Linear algebraic groups and related topics -- Linear algebraic groups and related topics; Representations of groups; Representations of algebras
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."--Page 4 of cover.
Notes: Includes bibliographical references (p. 217-223) and index.