Overview

This book is an introduction to the theory of quiver representations and quiver varieties, starting with basic definitions and ending with Nakajima's work on quiver varieties and the geometric realization of Kac–Moody Lie algebras. The first part of the book is devoted to the classical theory of quivers of finite type. Here the exposition is mostly self-contained and all important proofs are presented in detail. The second part contains the more recent topics of quiver theory that are related to quivers of infinite type: Coxeter functor, tame and wild quivers, McKay correspondence, and representations of Euclidean quivers. In the third part, topics related to geometric aspects of quiver theory are discussed, such as quiver varieties, Hilbert schemes, and the geometric realization of Kac–Moody algebras. Here some of the more technical proofs are omitted; instead only the statements and some ideas of the proofs are given, and the reader is referred to original papers for details. The exposition in the book requires only a basic knowledge of algebraic geometry, differential geometry, and the theory of Lie groups and Lie algebras. Some sections use the language of derived categories; however, the use of this language is reduced to a minimum. The many examples make the book accessible to graduate students who want to learn about quivers, their representations, and their relations to algebraic geometry and Lie algebras.

Full Product Details

Author:   Alexander Kirillov, Jr.
Publisher:   American Mathematical Society
Imprint:   American Mathematical Society
Weight:   0.707kg
ISBN:  

9781470423070

ISBN 10:   1470423073
Pages:   295
Publication Date:   30 October 2016
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us.

Table of Contents

Part 1. Dynkin Quivers Chapter 1. Basic Theory Chapter 2. Geometry of Orbits Chapter 3. Gabriel’s Theorem Chapter 4. Hall Algebras Chapter 5. Double Quivers Part 2. Quivers of Infinite Type Chapter 6. Coxeter Functor and Preprojective Representations Chapter 7. Tame and Wild Quivers Chapter 8. McKay Correspondence and Representations of Euclidean Quivers Chapter 9. Hamiltonian Reduction and Geometric Invariant Theory Chapter 10. Quiver Varieties Chapter 11. Jordan Quiver and Hilbert Schemes Chapter 12. Kleinian Singularities and Geometric McKay Correspondence Chapter 13. Geometric Realization of Kac–Moody Lie Algebras Appendix Bibliography

Reviews

With an adequate background in Lie theory and algebraic geometry, the book is accessible to an interested reader...it engages the reader to fill in some arguments or to look for a result in the references. As such, the book can be used for a topics course on its subjects. -Felipe Zaldivar, MAA Reviews

"The book should serve as a valuable source for readers who want to understand various levels of deep connections between quiver representations, Lie theory, quantum groups, and geometric representation theory...The beautiful results discussed in the present book touch on several mathematical areas, therefore, the inclusion of background material and several examples make it convenient to learn the subject."" - Mátyás Domokos, Mathematical Reviews ""With an adequate background in Lie theory and algebraic geometry, the book is accessible to an interested reader... it engages the reader to fill in some arguments or to look for a result in the references. As such, the book can be used for a topics course on its subjects."" - Felipe Zaldivar, MAA Reviews ""...a concise guide to representation theory of quiver representations for beginner and advanced researchers."" - Justyna Kosakowska, Zentralblatt Math"

With an adequate background in Lie theory and algebraic geometry, the book is accessible to an interested reader...it engages the reader to fill in some arguments or to look for a result in the references. As such, the book can be used for a topics course on its subjects. -Felipe Zaldivar, MAA Reviews ...a concise guide to representation theory of quiver representations for beginner and advanced researchers. -Justyna Kosakowska, Zentralblatt Math

Author Information

Alexander Krillov stony Brook University, NY

Tab Content 6

Author Website:  

Customer Reviews

Recent Reviews

No review item found!

Add your own review!

Countries Available

All regions