Skip to main content

Introduction to the Representation Theory of Algebras

  • Textbook
  • © 2015


  • A down-to-earth approach to the subject
  • Introduces all established descriptions within the field
  • Provides detailed and comprehensible proofs for all statements
  • Contains numerous exercises within the chapters
  • Includes supplementary material:

This is a preview of subscription content, log in via an institution to check access.

Access this book

eBook USD 34.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 44.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (9 chapters)


About this book

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, explaining 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.


“This book is a short and elementary course in the representation theory of finite dimensional algebras. It may be a good text book for undergraduate and PhD students, because only the knowledge of linear algebra is required.” (Justyna Kosakowska, zbMATH 1330.16001, 2016)

“Barot (former researcher, Instituto de Matemáticas, Univ. Nacional Autónoma de México) paints the big picture and emphasizes recent perspectives. … An advanced undergraduate could read this book as a wonderful case study in the power of shifting viewpoints and thus an initiation into the modern practice of mathematics. … Summing Up: Highly recommended. Lower- and upper-division undergraduates, graduate students, researchers/faculty, and professionals/practitioners.” (D. V. Feldman, Choice, Vol. 53 (4), December, 2015)

“The book gives a first introduction to the representation theory of finite-dimensional algebras over an algebraically closed field. … With its well-chosen topics, arranged in a smooth and attractive order, the book is highly recommended as a one-semester introductory course on representations of finite-dimensional algebras.” (Wolfgang Rump, Mathematical Reviews, October, 2015)

Authors and Affiliations

  • Instituto de Matemáticas, Universidad Nacional Autónoma de México, Mexico City, Mexico

    Michael Barot

About the author

Michael Barot was a researcher at the Instituto de Matemáticas of the Universidad Nacional Autónoma de México.

Bibliographic Information

Publish with us