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Quiver Representations

  • Ralf Schiffler

Part of the CMS Books in Mathematics book series (CMSBM)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Quivers and Their Representations

    1. Front Matter
      Pages 1-1
    2. Ralf Schiffler
      Pages 3-31
    3. Ralf Schiffler
      Pages 33-68
    4. Ralf Schiffler
      Pages 69-105
  3. Path Algebras

    1. Front Matter
      Pages 107-107
    2. Ralf Schiffler
      Pages 109-131
    3. Ralf Schiffler
      Pages 133-151
    4. Ralf Schiffler
      Pages 153-173
    5. Ralf Schiffler
      Pages 175-201
    6. Ralf Schiffler
      Pages 203-222
  4. Back Matter
    Pages 223-230

About this book

Introduction

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.

Keywords

Associative algebra Auslander-Reiten theory Gabriel's theorem Module Quiver representation

Authors and affiliations

  • Ralf Schiffler
    • 1
  1. 1.Department of MathematicsUniversity of ConnecticutStorrsUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-09204-1
  • Copyright Information Springer International Publishing Switzerland 2014
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-09203-4
  • Online ISBN 978-3-319-09204-1
  • Series Print ISSN 1613-5237
  • Series Online ISSN 2197-4152
  • Buy this book on publisher's site
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