An introduction to quiver representations

Author(s)

• Derksen, Harm
• Weyman, Jerzy

Bibliographic Information

An introduction to quiver representations

Harm Derksen, Jerzy Weyman

（Graduate studies in mathematics, v. 184）

American Mathematical Society, c2017

Note

Includes bibliographical references (p. 331-334) and index

Description and Table of Contents

Description

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 Auslander-Reiten 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 Auslander-Reiten theory, including almost split sequences and the Auslander-Reiten 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 semi-invariants of quiver representations and its application to Littlewood-Richardson 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 learn about application of quiver representations to their fields.

Table of Contents

Introduction Homological algebra of quiver representations Finite dimensional algebras Gabriel's theorem Almost split sequences Auslander-Reiten theory Extended Dynkin quivers Kac's theorem Geometric invariant theory Semi-invariants of quiver representations Orthogonal categories and exceptional sequences Cluster categories Notation Index Bibliography

by "Nielsen BookData"

Details

• NCID: BB25065721
• ISBN:
  • 9781470425562
• LCCN: 2017016426
• Country Code: us
• Title Language Code: eng
• Text Language Code: eng
• Place of Publication: Providence, R.I.
• Pages/Volumes: x, 334 p.
• Size: 27 cm
• Classification:
  • LCC : QA166.15
  • DC23 : 512/.46
• Subject Headings:
  • LCSH : Directed graphs
  • LCSH : Representations of graphs
  • LCSH : Vector spaces
• Parent Bibliography ID:
  • BA20542214