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Introduction to the Representation Theory of Algebras

  • Michael Barot

Table of contents

  1. Front Matter
    Pages i-x
  2. Michael Barot
    Pages 1-14
  3. Michael Barot
    Pages 15-31
  4. Michael Barot
    Pages 33-52
  5. Michael Barot
    Pages 53-71
  6. Michael Barot
    Pages 73-92
  7. Michael Barot
    Pages 93-112
  8. Michael Barot
    Pages 113-128
  9. Michael Barot
    Pages 129-145
  10. Michael Barot
    Pages 147-166
  11. Back Matter
    Pages 167-179

About this book

Introduction

This book gives a general introduction to the theory of representations of algebras. It starts with examples of classification problems of matrices under linear transformations and explains the three common setups: representation of quivers, modules over algebras and additive functors over certain categories. The main part is devoted to (i) module categories, presenting the unicity of the decomposition into indecomposable modules, the Auslander–Reiten theory and the technique of knitting; (ii) the use of combinatorial tools such as dimension vectors and integral quadratic forms; and (iii) deeper theorems such as Gabriel‘s Theorem, the trichotomy and the Theorem of Kac – all accompanied by further examples.
Each section includes exercises to facilitate understanding. By keeping the proofs as basic and comprehensible as possible and introducing the three languages at the beginning, this book is suitable for readers from the advanced undergraduate level onwards and enables them to consult related, specific research articles.

Keywords

Auslander-Reiten theory Combinatorial invariants Module categories Representations of algebras Representations of quivers

Authors and affiliations

  • Michael Barot
    • 1
  1. 1.Instituto de MatemáticasUniversidad Nacional Autónoma de MéxicoMexico CityMexico

Bibliographic information