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Algebras and Representation Theory

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Algebras and Representation Theory by Karin Erdmann

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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-Hoelder 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.

Author Biography

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 Universitat Hannover. His research interests include representation theory of finite groups and finite-dimensional algebras, and algebraic combinatorics.
Release date NZ
November 19th, 2018
Country of Publication
1st ed. 2018
2 Illustrations, black and white; X, 290 p. 2 illus.
Springer International Publishing AG
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