Authors:
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
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Table of contents (9 chapters)
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Front Matter
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Back Matter
About this book
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.
Reviews
“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)
Authors and Affiliations
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Instituto de Matemáticas, Universidad Nacional Autónoma de México, Mexico City, Mexico
Michael Barot
About the author
Bibliographic Information
Book Title: Introduction to the Representation Theory of Algebras
Authors: Michael Barot
DOI: https://doi.org/10.1007/978-3-319-11475-0
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing Switzerland 2015
Softcover ISBN: 978-3-319-11474-3Published: 14 January 2015
eBook ISBN: 978-3-319-11475-0Published: 29 December 2014
Edition Number: 1
Number of Pages: X, 179
Number of Illustrations: 109 b/w illustrations
Topics: Associative Rings and Algebras, Category Theory, Homological Algebra, General Algebraic Systems