Quiver Representations and Quiver Varieties
Author(s) (Product display):
Alexander Kirillov, Jr.
Stony Brook University, Stony Brook, NY
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.
Book Series Name:
Graduate Studies in Mathematics
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Expected publication date October 30, 2016