Introduction to the Representation Theory of Algebras

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9783319114743: Introduction to the Representation Theory of Algebras
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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.

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About the Author:

Michael Barot was a researcher at the Instituto de Matemáticas of the Universidad Nacional Autónoma de México.

Review:

“This book is a short and elementary course in the representation theory of finite dimensional algebras. It may be a good text book for undergraduate and PhD students, because only the knowledge of linear algebra is required.” (Justyna Kosakowska, zbMATH 1330.16001, 2016)

“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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Book Description Condition: New. Publisher/Verlag: Springer, Berlin | 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. | Matrix Problems.- Representations of Quivers.- Algebras.- Module Categories.- Elements of Homological Algebra.- The Auslander-Reiten Theory.- Knitting.- Combinatorial Invariants.- Indecomposables and Dimensions. | Format: Paperback | Language/Sprache: english | 302 gr | 235x154x10 mm | 179 pp. Seller Inventory # K9783319114743

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Book Description Springer-Verlag Gmbh Feb 2015, 2015. Taschenbuch. Condition: Neu. Neuware - 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. 179 pp. Englisch. Seller Inventory # 9783319114743

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Book Description Springer. Paperback. Condition: New. 184 pages. 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 AuslanderReiten 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 Gabriels 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. This item ships from multiple locations. Your book may arrive from Roseburg,OR, La Vergne,TN. Paperback. Seller Inventory # 9783319114743

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Book Description Springer-Verlag Gmbh Feb 2015, 2015. Taschenbuch. Condition: Neu. Neuware - 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. 179 pp. Englisch. Seller Inventory # 9783319114743

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