An Introduction to Quiver Representations (Graduate Studies in Mathematics) - Hardcover

Harm Derksen (author)|Jerzy Weyman (author)

Hardcover

ISBN 10: 1470425564 ISBN 13: 9781470425562

Publisher: American Mathematical Society, 2018

Synopsis

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.

About this title

About the Author

Harm Derksen, University of Michigan, Ann Arbor, MI.

Jerzy Weyman, University of Connecticut, Storrs, CT.

Edition details

• Publisher: American Mathematical Society
• Publication date: 2018
• Language: English
• ISBN 10: 1470425564
• ISBN 13: 9781470425562
• Binding: Hardcover
• Number of pages: 344