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Graduate Studies in Mathematics Ser.: Quiver Representations and Quiver Varieties by Alexander Kirillov (2016, Hardcover)

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QUIVER REPRESENTATIONS AND QUIVER VARIETIES (GRADUATE STUDIES IN MATHEMATICS) By Alexander Kirillov - Hardcover **BRAND NEW**.

About this product

Product Identifiers

PublisherAmerican Mathematical Society

ISBN-101470423073

ISBN-139781470423070

eBay Product ID (ePID)224565043

Product Key Features

Number of Pages296 Pages

Publication NameQuiver Representations and Quiver Varieties

LanguageEnglish

Publication Year2016

SubjectGraphic Methods, Algebra / General

TypeTextbook

Subject AreaMathematics

AuthorAlexander Kirillov

SeriesGraduate Studies in Mathematics Ser.

FormatHardcover

Dimensions

Item Height0.8 in

Item Weight24.7 Oz

Item Length10.3 in

Item Width7.4 in

Additional Product Features

Intended AudienceScholarly & Professional

LCCN2016-018803

ReviewsThe 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

Dewey Edition23

Series Volume Number174

IllustratedYes

Dewey Decimal512/.46

Table Of ContentPart 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

SynopsisThis 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., Provides 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 exposition in the book requires only a basic knowledge of algebraic geometry, differential geometry, and the theory of Lie groups and Lie algebras.

LC Classification NumberQA166.15.K75 2016