Reconstruction algebras of type D (II)

This is the third in a series of papers which give an explicit description of the reconstruction algebra as a quiver with relations; these algebras arise naturally as geometric generalizations of preprojective algebras of extended Dynkin quivers. This paper is the companion to [W12] and deals with dihedral groups G = DDn,q which have rank two special CM modules. We show that such reconstruction algebras are described by combining a preprojective algebra of type D~D~ with some reconstruction algebra of type A