Quiver representations and quiver varieties (Q2826212)

The book has three parts. The first is an elementary introduction to theory of representations of quivers. In this part, many aspects of representation theory of Dynkin quivers are described: Euler forms, root lattices, projective and injective modules, geometry of orbits of certain group actions on the representation space, Gabriel theorem, Hall algebras and preprojective algebras.NEWLINENEWLINEIn the second part, representation theory of infinite type quivers is discussed. In particular, the author describes preprojective and preinjective representations, Auslander-Reiten quivers, tame and wild quivers, tame-wild dichotomy, Kac's theorem.NEWLINENEWLINEThe third part is an excursion in quiver varieties theory. This part is more advanced. It contains for example: Hamiltonian reduction and geometric invariant theory, Hilbert schemes, Kleinian singularities, geometric McKay correspondence, geometric realization of Kac-Moody algebras.NEWLINENEWLINEThe book can be a concise guide to representation theory of quiver representations for beginner and advanced researchers.