An Introduction to Quiver Representations
Seiten
2018
American Mathematical Society (Verlag)
978-1-4704-2556-2 (ISBN)
American Mathematical Society (Verlag)
978-1-4704-2556-2 (ISBN)
Provides 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 book is suitable for a graduate course in quiver representations and has numerous exercises and examples throughout.
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.
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.
Harm Derksen, University of Michigan, Ann Arbor, MI. Jerzy Weyman, University of Connecticut, Storrs, CT.
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
| Erscheinungsdatum | 31.01.2018 |
|---|---|
| Reihe/Serie | Graduate Studies in Mathematics |
| Verlagsort | Providence |
| Sprache | englisch |
| Maße | 178 x 254 mm |
| Gewicht | 760 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Algebra |
| ISBN-10 | 1-4704-2556-4 / 1470425564 |
| ISBN-13 | 978-1-4704-2556-2 / 9781470425562 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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