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Springer Undergraduate Mathematics Series

Algebras and Representation Theory

Authors: Erdmann, Karin, Holm, Thorsten

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  • Offers an elementary introduction that includes more advanced topics such as Gabriel’s theorem on quivers
  • Based on the authors’ extensive undergraduate teaching experience
  • Provides numerous worked examples and more than 200 exercises (with worked solutions to some of them)
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eBook 29,74 €
price for Spain (gross)
  • ISBN 978-3-319-91998-0
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover 36,39 €
price for Spain (gross)
  • ISBN 978-3-319-91997-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
About this Textbook

This carefully written textbook provides an accessible introduction to the representation theory of algebras, including representations of quivers.

The book starts with basic topics on algebras and modules, covering fundamental results such as the Jordan-Hölder theorem on composition series, the Artin-Wedderburn theorem on the structure of semisimple algebras and the Krull-Schmidt theorem on indecomposable modules. The authors then go on to study representations of quivers in detail, leading to a complete proof of Gabriel's celebrated theorem characterizing the representation type of quivers in terms of Dynkin diagrams.

Requiring only introductory courses on linear algebra and groups, rings and fields, this textbook is aimed at undergraduate students. With numerous examples illustrating abstract concepts, and including more than 200 exercises (with solutions to about a third of them), the book provides an example-driven introduction suitable for self-study and use alongside lecture courses.

About the authors

Karin Erdmann's research focus lies on representation theory of finite groups, and finite-dimensional algebras. She has written many research articles, and is the author of a research monograph and a textbook.

Thorsten Holm is Professor of Mathematics at Leibniz Universität Hannover. His research interests include representation theory of finite groups and finite-dimensional algebras, and algebraic combinatorics.

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Table of contents (12 chapters)

Table of contents (12 chapters)
  • Algebras

    Pages 1-27

    Erdmann, Karin (et al.)

  • Modules and Representations

    Pages 29-59

    Erdmann, Karin (et al.)

  • Simple Modules and the Jordan–Hölder Theorem

    Pages 61-84

    Erdmann, Karin (et al.)

  • Semisimple Modules and Semisimple Algebras

    Pages 85-102

    Erdmann, Karin (et al.)

  • The Structure of Semisimple Algebras: The Artin–Wedderburn Theorem

    Pages 103-116

    Erdmann, Karin (et al.)

Buy this book

eBook 29,74 €
price for Spain (gross)
  • ISBN 978-3-319-91998-0
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover 36,39 €
price for Spain (gross)
  • ISBN 978-3-319-91997-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Algebras and Representation Theory
Authors
Series Title
Springer Undergraduate Mathematics Series
Copyright
2018
Publisher
Springer International Publishing
Copyright Holder
Springer Nature Switzerland AG
eBook ISBN
978-3-319-91998-0
DOI
10.1007/978-3-319-91998-0
Softcover ISBN
978-3-319-91997-3
Series ISSN
1615-2085
Edition Number
1
Number of Pages
IX, 298
Number of Illustrations
59 b/w illustrations
Topics