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Introduction to the representation t...

Barot, Michael.

Introduction to the representation theory of algebras

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Introduction to the representation theory of algebrasby Michael Barot.
作者:	Barot, Michael.
出版者:	Cham :Springer International Publishing :2015.
面頁冊數:	x, 179 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
標題:	Representations of algebras.
電子資源:	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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245 1 0 $a Introduction to the representation theory of algebras $h [electronic resource] / $c by Michael Barot.
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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.
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650 1 4 $a Mathematics. $3 184409
650 2 4 $a Associative Rings and Algebras. $3 274818
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