Introduction to the Representation Theory of Algebras
Barot, Michael
Produktnummer:
18af953530536e4abb9e31355f1fd6cb46
| Autor: | Barot, Michael |
|---|---|
| Themengebiete: | Auslander-Reiten theory Combinatorial invariants Module categories Representations of algebras Representations of quivers |
| Veröffentlichungsdatum: | 14.01.2015 |
| EAN: | 9783319114743 |
| Sprache: | Englisch |
| Seitenzahl: | 179 |
| Produktart: | Kartoniert / Broschiert |
| Verlag: | Springer International Publishing |
Produktinformationen "Introduction to the Representation Theory of Algebras"
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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