This book gives a general introduction to the theory of
representations of algebras. It starts with examples of
classification problems of matrices under linear transformations,
explaining the three common setups: representation of quivers,
modules over algebras and additive functors over certain
categories. The main part is devoted to (i) module categories,
presenting the unicity of the decomposition into indecomposable
modules, the Auslander-Reiten theory and the technique of knitting;
(ii) the use of combinatorial tools such as dimension vectors and
integral quadratic forms; and (iii) deeper theorems such as
Gabriel's Theorem, the trichotomy and the Theorem of Kac - all
accompanied by further examples. Each section includes exercises to
facilitate understanding. By keeping the proofs as basic and
comprehensible as possible and introducing the three languages at
the beginning, this book is suitable for readers from the advanced
undergraduate level onwards and enables them to consult related,
specific research articles.
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