Representation Theory: A Categorical Approach - cover image

Copyright

Jan E. Grabowski;

Published On

2025-09-22

ISBN

Paperback978-1-80511-714-8
Hardback978-1-80511-715-5
PDF978-1-80511-716-2

Language

  • English

Print Length

233 pages (viii+225)

Dimensions

Paperback156 x 13 x 234 mm(6.14" x 0.51" x 9.21")
Hardback156 x 14 x 234 mm(6.14" x 0.55" x 9.21")

Weight

Paperback335g (11.82oz)
Hardback507g (17.88oz)

OCLC Number

1540662569

LCCN

2025465564

THEMA

  • PBF
  • PBK
  • PBW
  • PHU

BISAC

  • MAT002000
  • MAT002010
  • MAT014000
  • MAT017000

LCC

  • QA176

Keywords

  • Representation Theory of Finite Groups
  • Representation Theory of Algebras
  • Representation Theory
  • Advanced Algebra
  • Mathematics
  • Mathematics textbook

Representation Theory

A Categorical Approach

  • Jan E. Grabowski (author)
This volume offers a fresh and modern introduction to one of abstract algebra’s key topics. Guiding readers through the transition between structure theory and representation theory, this textbook explores how algebraic objects like groups and rings act as symmetries of other structures. Using the accessible yet powerful language of category theory, the book reimagines standard approaches to topics such as modules and algebras in a way that unlocks modern treatments of more advanced topics such as quiver representations and even representations of Hopf algebras and categories.

Aimed at undergraduate students with prior exposure to linear algebra and basic group theory, the book introduces categories early and uses them throughout, providing a cohesive framework that mirrors current mathematical research. Though technically sophisticated, it also includes examples and exercises designed to develop intuition and understanding.

Grabowski’s inclusion of computational tools such as SageMath offers a valuable and traditionally underdeveloped bridge between abstract theory and hands-on exploration. This is a uniquely valuable guide for students ready to stretch their understanding of the subject’s conceptual depth and evolving frontiers.

Additional Resources

[book]HTML edition

The HTML edition for this book is available at https://www.maths.lancs.ac.uk/~grabowsj/. The HTML may be updated after publication.

[website]Errata page

This page lists corrections to the text that have been notified to the author.

Contents

Introduction

(pp. v–vi)
  • Jan E. Grabowski

1. Algebra

(pp. 1–70)
  • Jan E. Grabowski

2. Categories

(pp. 71–88)
  • Jan E. Grabowski

3. Representations

(pp. 89–108)
  • Jan E. Grabowski

4. Modules

(pp. 109–146)
  • Jan E. Grabowski

5. Examples

(pp. 147–194)
  • Jan E. Grabowski

6. Advanced topics

(pp. 195–210)
  • Jan E. Grabowski

Contributors

Jan E. Grabowski

(author)
Professor of Algebra at Lancaster University
https://www.maths.lancs.ac.uk/~grabowsj/

Jan Grabowski is an experienced researcher and educator in mathematics, with over 20 years’ experience of both, and currently holds the position of Professor of Algebra at Lancaster University. Jan has a strong research track record of publications in algebra and related topics, both as a single author and collaboratively. He has taught courses at Oxford and Lancaster across a range of levels and has been teaching abstract algebra for the majority of this time, including covering aspects of the material in the book in courses at both institutions. Jan has had recognition for his teaching, including a teaching prize at Oxford, obtaining a Postgraduate Certificate in Academic Practice and being awarded Senior Fellowship of the Higher Education Academy. He has championed innovation in teaching by presenting a mature exposition of ‘how mathematicians really think about these things’ as compared with other approaches that often defer more advanced ideas or techniques, rather than encouraging students to engage with challenging ideas early and repeatedly.