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Quiver representations and quiver varieties / Alexander Kirillov, Jr.

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Bibliographic Details
Main Author: Kirillov, Alexander A., 1967- (Author)
Format: Book
Language:English
Published: Providence, Rhode Island : American Mathematical Society, [2016]
Series:Graduate studies in mathematics ; v. 174.
Graduate studies in mathematics ; 174.
Subjects:
Directed graphs.
Representations of graphs.
Graph theory.
Associative rings and algebras > Representation theory of rings and algebras > Representations of quivers and partially ordered sets.
Algebraic geometry > Cycles and subschemes > Parametrization (Chow and Hilbert schemes)
Algebraic geometry > Families, fibrations > Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory)
Associative rings and algebras > Representation theory of rings and algebras > Representation type (finite, tame, wild, etc.)
Associative rings and algebras > Representation theory of rings and algebras > Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers.
Nonassociative rings and algebras > Lie algebras and Lie superalgebras > Representations, algebraic theory (weights)
Nonassociative rings and algebras > Lie algebras and Lie superalgebras > Root systems.
Nonassociative rings and algebras > Lie algebras and Lie superalgebras > Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras.
Table of Contents:
  • Basic theory
  • Geometry of orbits
  • Gabriel's theorem
  • Hall algebras
  • Double quivers
  • Coxeter functor and preprojective representations
  • Tame and wild quivers
  • McKay correspondence and representations
  • Hamiltonian reduction and geometric invariant theory
  • Quiver varieties
  • Jordan quiver and Hilbert schemes
  • Kleinian singularities and geometric McKay correspondence
  • Kac-Moody algebras and Weyl groups.

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