Titlebook: Algebras and Representation Theory; Karin Erdmann,Thorsten Holm Textbook 2018 Springer Nature Switzerland AG 2018 MSC (2010) 16-XX, 16G10,

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Representations of Quivers,to modules for its path algebra. In this chapter we develop the theory further and study representations of quivers in detail. In particular we show how to exploit properties which come from the graph structure of the quiver.

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Diagrams and Roots, the relevant graphs. They are known as Dynkin diagrams and Euclidean diagrams, these occur in many parts of mathematics. We introduce roots, and we discuss further tools needed later, such as the Coxeter transformations. The content of this chapter is mainly basic combinatorics and linear algebra.

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Textbook 2018he 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 stud

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Textbook 2018uate 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..

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Modules and Representations,tion. Perhaps the most elementary way to think of modules is to view them as generalizations of vector spaces, where the role of scalars is played by elements in an algebra, or more generally, in a ring. We introduce many examples, and study the fundamental notions of submodules, factor modules and

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Semisimple Modules and Semisimple Algebras,mple modules. In this chapter we study modules which are direct sums of simple modules, this leads to the theory of semisimple modules. For some algebras, every module is a direct sum of simple modules. These algebras are said to be semisimple, and they have important applications. In this chapter,

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,The Structure of Semisimple Algebras: The Artin–Wedderburn Theorem, matrix algebras are semisimple algebras. When the coefficient field is algebraically closed the Artin-Wedderburn theorem shows that every semisimple algebra is isomorphic to such an algebra. In general, a semisimple algebra is isomorphic to a direct product of matrix algebras but where matrix block