Introduction to the Representation Theory of Algebras (PDF)
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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 and explains 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.
- Autor: Michael Barot
- 2014, 2015, 179 Seiten, Englisch
- Verlag: Springer-Verlag GmbH
- ISBN-10: 3319114751
- ISBN-13: 9783319114750
- Erscheinungsdatum: 29.12.2014
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- Dateiformat: PDF
- Grösse: 6.47 MB
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“Barot (former researcher, Instituto de Matemáticas, Univ. Nacional Autónoma de México) paints the big picture and emphasizes recent perspectives. … An advanced undergraduate could read this book as a wonderful case study in the power of shifting viewpoints and thus an initiation into the modern practice of mathematics. … Summing Up: Highly recommended. Lower- and upper-division undergraduates, graduate students, researchers/faculty, and professionals/practitioners.” (D. V. Feldman, Choice, Vol. 53 (4), December, 2015)
“The book gives a first introduction to the representation theory of finite-dimensional algebras over an algebraically closed field. … With its well-chosen topics, arranged in a smooth and attractive order, the book is highly recommended as a one-semester introductory course on representations of finite-dimensional algebras.” (Wolfgang Rump, Mathematical Reviews, October, 2015)
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