Reconstruction Algebras of Type D (I)

Details Reconstruction Algebras of Type D (I) Reconstruction Algebras of Type D (I)

2009-05-08

arxiv.org/abs/0905.1154v2

Mathematics

Rings and Algebras

31 pages, final version

Scientific paper

This is the second 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 diagrams. This paper deals with dihedral groups G=D_{n,q} for which all special CM modules have rank one, and we show that all but four of the relations on such a reconstruction algebra are given simply as the relations arising from a reconstruction algebra of type A. As a corollary, the reconstruction algebra reduces the problem of explicitly understanding the minimal resolution (=G-Hilb) to the same level of difficulty as the toric case.

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