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 deals with dihedral groups G=D_{n,q} which have rank 2 special CM modules. We show that such reconstruction algebras are described by combining a preprojective algebra of extended type D with some reconstruction algebra of type A.