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arXiv · 0905.1154

Reconstruction Algebras of Type D (I)

M. Wemyss
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Abstract

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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M. Wemyss. 2012-02-09. Reconstruction Algebras of Type D (I). https://arxiv.org/abs/0905.1154

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