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Introduction to the representation t...

Barot, Michael.

Introduction to the representation theory of algebras

Record Type:	Electronic resources : Monograph/item
Title/Author:	Introduction to the representation theory of algebrasby Michael Barot.
Author:	Barot, Michael.
Published:	Cham :Springer International Publishing :2015.
Description:	x, 179 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Representations of algebras.
Online resource:	http://dx.doi.org/10.1007/978-3-319-11475-0
ISBN:	9783319114750 (electronic bk.)

Introduction to the representation theory of algebras
Barot, Michael.

Introduction to the representation theory of algebras[electronic resource] /by Michael Barot. - Cham :Springer International Publishing :2015. - x, 179 p. :ill., digital ;24 cm.

Matrix Problems -- Representations of Quivers -- Algebras -- Module Categories -- Elements of Homological Algebra -- The Auslander-Reiten Theory -- Knitting -- Combinatorial Invariants -- Indecomposables and Dimensions.

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.

ISBN: 9783319114750 (electronic bk.)

Standard No.: 10.1007/978-3-319-11475-0doiSubjects--Topical Terms:

191077
Representations of algebras.

LC Class. No.: QA155

Dewey Class. No.: 512.2

Introduction to the representation theory of algebras
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100 1 $a Barot, Michael. $3 713095
245 1 0 $a Introduction to the representation theory of algebras $h [electronic resource] / $c by Michael Barot.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2015.
300 $a x, 179 p. : $b ill., digital ; $c 24 cm.
505 0 $a Matrix Problems -- Representations of Quivers -- Algebras -- Module Categories -- Elements of Homological Algebra -- The Auslander-Reiten Theory -- Knitting -- Combinatorial Invariants -- Indecomposables and Dimensions.
520 $a 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.
650 0 $a Representations of algebras. $3 191077
650 1 4 $a Mathematics. $3 184409
650 2 4 $a Associative Rings and Algebras. $3 274818
650 2 4 $a Category Theory, Homological Algebra. $3 275954
650 2 4 $a General Algebraic Systems. $3 275666
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950 $a Mathematics and Statistics (Springer-11649)