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OverviewThis 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. Full Product DetailsAuthor: Karin Erdmann , Thorsten HolmPublisher: Springer International Publishing AG Imprint: Springer International Publishing AG Edition: 1st ed. 2018 Weight: 0.474kg ISBN: 9783319919973ISBN 10: 3319919970 Pages: 298 Publication Date: 26 September 2018 Audience: College/higher education , Undergraduate Format: Paperback Publisher's Status: Active Availability: Manufactured on demand  We will order this item for you from a manufactured on demand supplier. Table of Contents1 Introduction.- 2 Algebras.- 3 Modules and Representations.- 4 Simple Modules in the Jordan-Hölder Theorem.- 5 Semisimple Modules and Semisimple Algebras.- 6 The Structure of Semisimple ALgebras - The Artin-Wedderburn Theorem.- 7 Semisimple Group Algebras and Maschke's Theorem.- 8 Indecomposable Modules.- 9 Representation Type.- 10 Representations of Quivers.- 11 Diagrams and Roots.- 12 Gabriel's Theorem.- 13 Proofs and Background.- 14 Appendix A: Induced Modules for Group Algebras.- 15 Appendix B: Solutions to Selected Exercises.- Index.Reviews“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) 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) Author InformationKarin 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. Tab Content 6Author Website:Countries AvailableAll regions |
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