Description
Introduction to the Representation Theory of Algebras, 2015
Author: Barot Michael
Language: EnglishSubject for Introduction to the Representation Theory of Algebras:
Approximative price 42.19 €
In Print (Delivery period: 15 days).
Add to cart the book of Barot Michael179 p. · 15.5x23.5 cm · Paperback
Description
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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.
A down-to-earth approach to the subject
Introduces all established descriptions within the field
Provides detailed and comprehensible proofs for all statements
Contains numerous exercises within the chapters
Includes supplementary material: sn.pub/extras