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portada Introduction to the Representation Theory of Algebras
Type
Physical Book
Author
Publisher
Language
English
Pages
179
Format
Paperback
Dimensions
23.4x15.6x1 cm
Weight
0.28 kg.
ISBN13
9783319114743
Edition No.
2015th
Categories

Introduction to the Representation Theory of Algebras

Michael Barot (Author) · Springer · Paperback

Introduction to the Representation Theory of Algebras - Barot, Michael

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Synopsis "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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