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)

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