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BL
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| Record Number
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850256
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| Main Entry
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Derksen, Harm,1970-
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| Title & Author
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An introduction to quiver representations /\ Harm Derksen, Jerzy Weyman.
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| Publication Statement
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Providence, Rhode Island :: American Mathematical Society,, [2017]
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| Series Statement
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Graduate studies in mathematics ;; 184
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| Page. NO
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x, 334 pages :: illustrations ;; 27 cm.
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| ISBN
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1470425564
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: 9781470425562
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| Bibliographies/Indexes
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Includes bibliographical references (pages 331-334) and index.
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| Contents
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Ch. 1. Introduction -- Ch. 2. Homological algebra of quiver representations -- Ch. 3. Finite dimensional algebras -- Ch. 4. Gabriel's theorem -- Ch. 5. Almost split sequences -- Ch. 6. Auslander-Reiten theory -- Ch. 7. Extended Dynkin quivers -- Ch. 8. Kac's theorem -- Ch. 9. Geometric Invariant Theory -- Ch. 10. Semi-invariants of quiver representations -- Ch. 11. Orthogonal categories and exceptional sequences -- Ch. 12. Cluster categories.
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| Abstract
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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 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 to learn about applications of quiver representations to their fields.
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| Subject
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Directed graphs.
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Representations of graphs.
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Vector spaces.
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Algebraic geometry-- Algebraic groups-- Geometric invariant theory.
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Associative rings and algebras-- Representation theory of rings and algebras-- Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers.
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Associative rings and algebras-- Representation theory of rings and algebras-- Representations of Artinian rings.
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Commutative algebra-- General commutative ring theory-- Actions of groups on commutative rings; invariant theory.
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Directed graphs.
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Representations of graphs.
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Vector spaces.
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| Dewey Classification
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512/.46
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| LC Classification
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QA166.15.D47 2017
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| NLM classification
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13A50.msc
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16G1016G7014L2413A50msc
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| Added Entry
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Weyman, Jerzy,1955-
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