CMS Books in Mathematics

Quiver Representations

Authors: Schiffler, Ralf

  • ​First textbook on representation theory which uses the quiver representations approach
  • Much shorter than other texts on the subject and is meant as a textbook for a one semester course
  • Explicit constructions of Auslander-Reiten quivers are given
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Buy this book

eBook $54.99
price for USA (gross)
  • ISBN 978-3-319-09204-1
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $69.99
price for USA
  • ISBN 978-3-319-09203-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $69.99
price for USA
  • Customers within the U.S. and Canada please contact Customer Service at 1-800-777-4643, Latin America please contact us at +1-212-460-1500 (Weekdays 8:30am – 5:30pm ET) to place your order.
  • Due: August 31, 2016
  • ISBN 978-3-319-36317-2
  • Free shipping for individuals worldwide
About this Textbook

This book is intended to serve as a textbook for a course in Representation Theory of Algebras at the beginning graduate level. The text has two parts. In Part I, the theory is studied in an elementary way using quivers and their representations. This is a very hands-on approach and requires only basic knowledge of linear algebra. The main tool for describing the representation theory of a finite-dimensional algebra is its Auslander-Reiten quiver, and the text introduces these quivers as early as possible. Part II then uses the language of algebras and modules to build on the material developed before. The equivalence of the two approaches is proved in the text. The last chapter gives a proof of Gabriel’s Theorem. The language of category theory is developed along the way as needed.

About the authors

Ralf Schiffler is a Professor in the Department of Mathematics at the University of Connecticut.

Reviews

“This book is an excellent text for undergraduates or beginning graduate students. The virtues of the book can be amplified by an instructor willing to go faster for those who have some prior exposure to basic algebra, or to go slower for students starting ab ovo. Secondly, a non-expert (in representation theory of quivers) may also benefit from this book in several ways … . a reader will enjoy the clear and concise overview preceding each chapter and section.” (Alex Martsinkovsky, Mathematical Reviews, February, 2016)

“The book under review is an elementary introduction to the diagrammatic or quiver approach to the representation theory of finite-dimensional algebras. It is perhaps the first such textbook addressed to advanced undergraduates or beginning graduate students. … Teaching a course from this book should be a pleasant experience. Sets of problems are provided at the end of every one of its chapters, and little notes point to the literature. For a motivated student, the book is well suited for self-study.” (Felipe Zaldivar, MAA Reviews, December, 2014)

Video

Table of contents (8 chapters)

Buy this book

eBook $54.99
price for USA (gross)
  • ISBN 978-3-319-09204-1
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $69.99
price for USA
  • ISBN 978-3-319-09203-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $69.99
price for USA
  • Customers within the U.S. and Canada please contact Customer Service at 1-800-777-4643, Latin America please contact us at +1-212-460-1500 (Weekdays 8:30am – 5:30pm ET) to place your order.
  • Due: August 31, 2016
  • ISBN 978-3-319-36317-2
  • Free shipping for individuals worldwide
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Bibliographic Information

Bibliographic Information
Book Title
Quiver Representations
Authors
Series Title
CMS Books in Mathematics
Copyright
2014
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-09204-1
DOI
10.1007/978-3-319-09204-1
Hardcover ISBN
978-3-319-09203-4
Softcover ISBN
978-3-319-36317-2
Series ISSN
1613-5237
Edition Number
1
Number of Pages
XI, 230
Number of Illustrations and Tables
357 b/w illustrations
Topics