Reconstruction Algebras of Type D (II)

TL;DR

This paper describes the structure of reconstruction algebras for dihedral groups of type D, combining preprojective algebras of type D with type A to generalize known algebraic structures.

Contribution

It provides an explicit quiver with relations description of these reconstruction algebras for dihedral groups with rank 2 special CM modules.

Findings

Reconstruction algebras for dihedral groups are characterized by combining type D and type A preprojective algebras.

Explicit quiver with relations description is provided for these algebras.

The work extends the understanding of reconstruction algebras in the context of dihedral groups.

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 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.