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Cover: 9783319114743 | Introduction to the Representation Theory of Algebras | Michael Barot
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Introduction to the Representation Theory of Algebras
Taschenbuch von Michael Barot
Sprache: Englisch

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Beschreibung
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.
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.
Über den Autor
Michael Barot was a researcher at the Instituto de Matemáticas of the Universidad Nacional Autónoma de México.
Zusammenfassung

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: [...]

Inhaltsverzeichnis
Matrix Problems.- Representations of Quivers.- Algebras.- Module Categories.- Elements of Homological Algebra.- The Auslander-Reiten Theory.- Knitting.- Combinatorial Invariants.- Indecomposables and Dimensions.
Details
Erscheinungsjahr: 2015
Fachbereich: Arithmetik & Algebra
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Seiten: 192
Inhalt: x
179 S.
109 s/w Illustr.
179 p. 109 illus.
ISBN-13: 9783319114743
ISBN-10: 3319114743
Sprache: Englisch
Herstellernummer: 86379821
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Barot, Michael
Auflage: 2015
Hersteller: Springer International Publishing
Maße: 235 x 155 x 11 mm
Von/Mit: Michael Barot
Erscheinungsdatum: 14.01.2015
Gewicht: 0,3 kg
preigu-id: 105160782
Über den Autor
Michael Barot was a researcher at the Instituto de Matemáticas of the Universidad Nacional Autónoma de México.
Zusammenfassung

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: [...]

Inhaltsverzeichnis
Matrix Problems.- Representations of Quivers.- Algebras.- Module Categories.- Elements of Homological Algebra.- The Auslander-Reiten Theory.- Knitting.- Combinatorial Invariants.- Indecomposables and Dimensions.
Details
Erscheinungsjahr: 2015
Fachbereich: Arithmetik & Algebra
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Seiten: 192
Inhalt: x
179 S.
109 s/w Illustr.
179 p. 109 illus.
ISBN-13: 9783319114743
ISBN-10: 3319114743
Sprache: Englisch
Herstellernummer: 86379821
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Barot, Michael
Auflage: 2015
Hersteller: Springer International Publishing
Maße: 235 x 155 x 11 mm
Von/Mit: Michael Barot
Erscheinungsdatum: 14.01.2015
Gewicht: 0,3 kg
preigu-id: 105160782
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