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Quiver Representations and Quiver Varieties

Alexander Kirillov (author)

ISBN: 9781470423070

Publication Date: Oct 2016

Format: Hardback

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.
£90.95

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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.

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
Pages 295
Dimensions 229 x 152
Date Published 30 Oct 2016
Publisher American Mathematical Society
Series Graduate Studies in Mathematics
Series Part 174
Subject/s Algebra   Algebraic geometry  
Alexander Krillov stony Brook University, NY

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