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＜E-Book＞
Algebras and Representation Theory / by Karin Erdmann, Thorsten Holm
(Springer Undergraduate Mathematics Series. ISSN:21974144)

Edition	1st ed. 2018.
Publisher	(Cham : Springer International Publishing : Imprint: Springer)
Year	2018
Size	IX, 298 p. 59 illus : online resource
Authors	*Erdmann, Karin author Holm, Thorsten author SpringerLink (Online service)
Subjects	LCSH:Associative rings LCSH:Associative algebras LCSH:Commutative algebra LCSH:Commutative rings LCSH:Group theory LCSH:Algebra, Homological FREE:Associative Rings and Algebras FREE:Commutative Rings and Algebras FREE:Group Theory and Generalizations FREE:Category Theory, Homological Algebra
Notes	1 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 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 HTTP:URL=https://doi.org/10.1007/978-3-319-91998-0

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