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Algebras and representation theory

Author: Karin Erdmann; Thorsten Holm
Publisher: Cham, Switzerland : Springer, 2018.
Series: Springer undergraduate mathematics series.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
"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 indecromposable  Read more...
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Genre/Form: Textbooks
Electronic books
Additional Physical Format: Print version:
Erdmann, Karin, 1948-
Algebras and representation theory.
Cham, Switzerland : Springer, [2018]
(DLC) 2018950191
(OCoLC)1032590267
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Karin Erdmann; Thorsten Holm
ISBN: 9783319919980 3319919989
OCLC Number: 1052613640
Description: 1 online resource (ix, 298 pages) : illustrations.
Contents: Algebras --
Models and representations --
Simple modules and the Jordan-Hölder theorem --
Seismographic modules and semisimple algebras --
The structure of semisimple algebras : the Artin-Wedderburn theorem --
Semisimple group algebras and Maschke's theorem --
Indecomposable modules --
Representation type --
Representations of quivers --
Diagrams and roots --
Gabriel's theorem --
Proofs and background --
Induced modules for group algebras --
Solutions to selected exercises.
Series Title: Springer undergraduate mathematics series.
Responsibility: Karin Erdmann, Thorsten Holm.

Abstract:

"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 indecromposable 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"--Print version, page 4 of cover.

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