Reconstruction algebras of type D (I)

Michael Wemyss*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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 pre-projective algebras of extended Dynkin diagrams. This paper deals with dihedral groups G = D-n,D-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. (C) 2012 Elsevier Inc. All rights reserved.

Original languageEnglish
Pages (from-to)158-194
Number of pages37
JournalJournal of Algebra
Volume356
Issue number1
DOIs
Publication statusPublished - 15 Apr 2012

Keywords

  • Noncommutative resolutions
  • CM modules
  • Surface singularities
  • MODULES
  • FLOPS
  • RINGS

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