Algebras and Representation Theory
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 Art...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | Englisch |
| Veröffentlicht: |
Cham :
Springer International Publishing,
2018.
|
| Ausgabe: | 1st ed. 2018. |
| Schriftenreihe: | Springer Undergraduate Mathematics Series,
|
| Schlagworte: | |
| ISBN: | 9783319919980 |
| ISSN: | 1615-2085 |
| Online-Zugang: |
|
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
MARC
| LEADER | 00000nam a22000005i 4500 | ||
|---|---|---|---|
| 003 | SK-BrCVT | ||
| 005 | 20220618114534.0 | ||
| 007 | cr nn 008mamaa | ||
| 008 | 180907s2018 gw | s |||| 0|eng d | ||
| 020 | |a 9783319919980 | ||
| 024 | 7 | |a 10.1007/978-3-319-91998-0 |2 doi | |
| 035 | |a CVTIDW06761 | ||
| 040 | |a Springer-Nature |b eng |c CVTISR |e AACR2 | ||
| 041 | |a eng | ||
| 100 | 1 | |a Erdmann, Karin. |4 aut | |
| 245 | 1 | 0 | |a Algebras and Representation Theory |h [electronic resource] / |c by Karin Erdmann, Thorsten Holm. |
| 250 | |a 1st ed. 2018. | ||
| 260 | 1 | |a Cham : |b Springer International Publishing, |c 2018. | |
| 300 | |a IX, 298 p. 59 illus. |b online resource. | ||
| 490 | 1 | |a Springer Undergraduate Mathematics Series, |x 1615-2085 | |
| 500 | |a Mathematics and Statistics | ||
| 505 | 0 | |a 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. | |
| 516 | |a text file PDF | ||
| 520 | |a 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. | ||
| 650 | 0 | |a Associative rings. | |
| 650 | 0 | |a Rings (Algebra). | |
| 650 | 0 | |a Commutative algebra. | |
| 650 | 0 | |a Commutative rings. | |
| 650 | 0 | |a Group theory. | |
| 650 | 0 | |a Category theory (Mathematics). | |
| 650 | 0 | |a Homological algebra. | |
| 856 | 4 | 0 | |u http://hanproxy.cvtisr.sk/han/cvti-ebook-springer-eisbn-978-3-319-91998-0 |y Vzdialený prístup pre registrovaných používateľov |
| 910 | |b ZE04041 | ||
| 919 | |a 978-3-319-91998-0 | ||
| 974 | |a andrea.lebedova |f Elektronické zdroje | ||
| 992 | |a SUD | ||
| 999 | |c 271579 |d 271579 | ||