On components of stable Auslander-Reiten quivers that contain Heller lattices: the case of truncated polynomial rings

2014/08/27 by Susumu Ariki, Ariki, Susumu, Ryoichi Kase +3
Mathematics · #FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA) #math.RA #math.RT

paper · pdf · doi:10.48550/arxiv.1408.6452

29 pages (v2) typo corrected (v3) several errors corrected (v4) modified some parts in subsections 1.3, 1.4 and 1.5

arxiv created 2018/03/30 · arxiv updated 2018/04/02

Abstract

Let A be a truncated polynomial ring over a complete discrete valuation ring O, and we consider the additive category consisting of A-lattices M with the property that M⊗ K is projective as an A⊗ K-module, where K is the fraction field of O. Then, we may define the stable Auslander-Reiten quiver of the category. We determine the shape of the components of the stable Auslander-Reiten quiver that contain Heller lattices.

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