Introduction to the representation theory of algebras [electronic resource] / Michael Barot.
Barot, Michael, author.
2015
QA155
Available Online

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Title Introduction to the representation theory of algebras [electronic resource] / Michael Barot.
Author Barot, Michael, author.
ISBN 9783319114750 electronic book
3319114751 electronic book
9783319114743
DOI https://doi.org/10.1007/978-3-319-11475-0
Published Cham : Springer, 2015.
Language English
Description 1 online resource (x, 179 pages) : illustrations
Item Number 10.1007/978-3-319-11475-0 doi
Call Number QA155
Dewey Decimal Classification 512/.2
Summary 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.
Bibliography, etc. Note Includes bibliographical references and indexes.
Access Note Access limited to authorized users.
Source of Description Online resource; title from PDF title page (SpringerLink, viewed January 19, 2015).
Available in Other Form Print version: 9783319114743
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Matrix Problems
Representations of Quivers
Algebras
Module Categories
Elements of Homological Algebra
The Auslander-Reiten Theory
Knitting
Combinatorial Invariants
Indecomposables and Dimensions.

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