Overview
- 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)
Part of the book series: Springer Undergraduate Mathematics Series (SUMS)
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Table of contents (12 chapters)
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Front Matter
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Back Matter
Keywords
About this book
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.
Reviews
Authors and Affiliations
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.
Bibliographic Information
Book Title: Algebras and Representation Theory
Authors: Karin Erdmann, Thorsten Holm
Series Title: Springer Undergraduate Mathematics Series
DOI: https://doi.org/10.1007/978-3-319-91998-0
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2018
Softcover ISBN: 978-3-319-91997-3Published: 26 September 2018
eBook ISBN: 978-3-319-91998-0Published: 07 September 2018
Series ISSN: 1615-2085
Series E-ISSN: 2197-4144
Edition Number: 1
Number of Pages: IX, 298
Number of Illustrations: 59 b/w illustrations
Topics: Associative Rings and Algebras, Commutative Rings and Algebras, Group Theory and Generalizations, Category Theory, Homological Algebra