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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.
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.
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.
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)
| Erscheinungsjahr: | 2018 |
|---|---|
| Fachbereich: | Arithmetik & Algebra |
| Genre: | Mathematik, Medizin, Naturwissenschaften, Technik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Taschenbuch |
| Reihe: | Springer Undergraduate Mathematics Series |
| Inhalt: |
ix
298 S. 59 s/w Illustr. 298 p. 59 illus. |
| ISBN-13: | 9783319919973 |
| ISBN-10: | 3319919970 |
| Sprache: | Englisch |
| Herstellernummer: | 978-3-319-91997-3 |
| Einband: | Kartoniert / Broschiert |
| Autor: |
Erdmann, Karin
Holm, Thorsten |
| Hersteller: |
Springer
Springer International Publishing AG Springer Undergraduate Mathematics Series |
| Verantwortliche Person für die EU: | Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com |
| Maße: | 235 x 155 x 17 mm |
| Von/Mit: | Karin Erdmann (u. a.) |
| Erscheinungsdatum: | 26.09.2018 |
| Gewicht: | 0,47 kg |
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