Introduction to the Representation Theory of Algebras

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Focusing on the theory of representations of algebras, this book introduces key concepts through examples of matrix classification under linear transformations. It covers representation of quivers, modules over algebras, and additive functors. Key topics include module categories, the uniqueness of indecomposable module decomposition, Auslander Reiten theory, and combinatorial tools like dimension vectors. Additionally, it explores significant theorems such as Gabriel's Theorem and Kac's Theorem, complemented by various examples to illustrate these concepts.