Algebras and Representation Theory
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Beschreibung
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.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.
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)
Autor*in
Karin Erdmann
Themen in »Algebras and Representation Theory«
MSC (2010) 16-XX, 16G10, 16G20, 16D10, 16D60, 16G60, 20CXX algebras representations modules simple modules Jordan-Hoelder theorem Artin-Wedderburn theorem Maschke's theorem indecomposable modules Krull-Schmidt theorem representation type representations of quivers Gabriel's theorem
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“The book under review is a text-book for higher undergraduate mathematics students or graduate students who have previous knowledge of results from linear algebra, and basic properties of rings and groups. … It is also useful for non-experts (in representation theory of quivers), they may benefit from this book in several ways: by examining the numerous worked examples, or by working out the many exercises.” (Bin Zhu, zbMATH 1429.16001, 2020)
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