Reconstruction algebras of type D (I)

Wemyss, M. (2012) Reconstruction algebras of type D (I). Journal of Algebra, 356(1), pp. 158-194. (doi:10.1016/j.jalgebra.2012.01.019)

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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=Dn,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.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Wemyss, Professor Michael
Authors: Wemyss, M.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Journal of Algebra
Publisher:Elsevier
ISSN:0021-8693
ISSN (Online):1090-266X
Published Online:09 February 2012
Copyright Holders:Copyright © 2012 Elsevier Inc.
First Published:First published in Journal of Algebra 356(1):158-194
Publisher Policy:Reproduced in accordance with the copyright policy of the publisher

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