Hardcover ISBN:  9781470425562 
Product Code:  GSM/184 
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eBook ISBN:  9781470442606 
Product Code:  GSM/184.E 
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AMS Member Price:  $68.00 
Hardcover ISBN:  9781470425562 
eBook: ISBN:  9781470442606 
Product Code:  GSM/184.B 
List Price:  $220.00 $177.50 
MAA Member Price:  $198.00 $159.75 
AMS Member Price:  $176.00 $142.00 
Hardcover ISBN:  9781470425562 
Product Code:  GSM/184 
List Price:  $135.00 
MAA Member Price:  $121.50 
AMS Member Price:  $108.00 
eBook ISBN:  9781470442606 
Product Code:  GSM/184.E 
List Price:  $85.00 
MAA Member Price:  $76.50 
AMS Member Price:  $68.00 
Hardcover ISBN:  9781470425562 
eBook ISBN:  9781470442606 
Product Code:  GSM/184.B 
List Price:  $220.00 $177.50 
MAA Member Price:  $198.00 $159.75 
AMS Member Price:  $176.00 $142.00 

Book DetailsGraduate Studies in MathematicsVolume: 184; 2017; 344 ppMSC: Primary 16; 14; 13
This book is an introduction to the representation theory of quivers and finite dimensional algebras. It gives a thorough and modern treatment of the algebraic approach based on AuslanderReiten theory as well as the approach based on geometric invariant theory. The material in the opening chapters is developed starting slowly with topics such as homological algebra, Morita equivalence, and Gabriel's theorem. Next, the book presents AuslanderReiten theory, including almost split sequences and the AuslanderReiten transform, and gives a proof of Kac's generalization of Gabriel's theorem. Once this basic material is established, the book goes on with developing the geometric invariant theory of quiver representations. The book features the exposition of the saturation theorem for semiinvariants of quiver representations and its application to LittlewoodRichardson coefficients. In the final chapters, the book exposes tilting modules, exceptional sequences and a connection to cluster categories.
The book is suitable for a graduate course in quiver representations and has numerous exercises and examples throughout the text. The book will also be of use to experts in such areas as representation theory, invariant theory and algebraic geometry, who want to learn about applications of quiver representations to their fields.
ReadershipGraduate students and researchers interested in representation theory, quivers, and applications to categories.

Table of Contents

Chapters

Introduction

Homological algebra of quiver representations

Finite dimensional algebras

Gabriel’s theorem

Almost split sequences

AuslanderReiten theory

Extended Dynkin quivers

Kac’s theorem

Geometric invariant theory

Semiinvariants of quiver representations

Orthogonal categories and exceptional sequences

Cluster categories


Additional Material

Reviews

This book serves as an introductory text on quiver representations which would allow a person without any knowledge of Artin algebras to learn the subject quickly.
Queqing Chen, Mathematical Reviews


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This book is an introduction to the representation theory of quivers and finite dimensional algebras. It gives a thorough and modern treatment of the algebraic approach based on AuslanderReiten theory as well as the approach based on geometric invariant theory. The material in the opening chapters is developed starting slowly with topics such as homological algebra, Morita equivalence, and Gabriel's theorem. Next, the book presents AuslanderReiten theory, including almost split sequences and the AuslanderReiten transform, and gives a proof of Kac's generalization of Gabriel's theorem. Once this basic material is established, the book goes on with developing the geometric invariant theory of quiver representations. The book features the exposition of the saturation theorem for semiinvariants of quiver representations and its application to LittlewoodRichardson coefficients. In the final chapters, the book exposes tilting modules, exceptional sequences and a connection to cluster categories.
The book is suitable for a graduate course in quiver representations and has numerous exercises and examples throughout the text. The book will also be of use to experts in such areas as representation theory, invariant theory and algebraic geometry, who want to learn about applications of quiver representations to their fields.
Graduate students and researchers interested in representation theory, quivers, and applications to categories.

Chapters

Introduction

Homological algebra of quiver representations

Finite dimensional algebras

Gabriel’s theorem

Almost split sequences

AuslanderReiten theory

Extended Dynkin quivers

Kac’s theorem

Geometric invariant theory

Semiinvariants of quiver representations

Orthogonal categories and exceptional sequences

Cluster categories

This book serves as an introductory text on quiver representations which would allow a person without any knowledge of Artin algebras to learn the subject quickly.
Queqing Chen, Mathematical Reviews