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Introduction to the Representation Theory of Algebras
Paperback
ISBN13: 9783319114743
Publisher: Springer Nature
Published: Jan 14 2015
Pages: 179
Weight: 0.61
Height: 0.41 Width: 6.14 Depth: 9.21
Language: English
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.
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