# Hokkaido Mathematical Journal

## Hokkaido Mathematical Journal, 42 (2013) pp.293-329

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### Abstract

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 = $\mathbb{D}$n,q which have rank two special CM modules. We show that such reconstruction algebras are described by combining a preprojective algebra of type $\tilde{D}$ with some reconstruction algebra of type A.

MSC(Primary) 13C14 14E16, 16S38 Noncommutative resolutions, CM modules, surface singularities