Algebras and Representation Theory
商品資訊
系列名：Springer Undergraduate Mathematics
ISBN13：9783319919973
出版社：Springer Nature
作者：Karin Erdmann; Thorsten Holm
出版日：2018/09/26
裝訂／頁數：平裝／298頁
規格：22.9cm*15.2cm*2.5cm (高/寬/厚)
商品簡介
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.
作者簡介
Karin 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 Universitat Hannover. His research interests include representation theory of finite groups and finite-dimensional algebras, and algebraic combinatorics.
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