Categories of lattices, and their global structure in terms of almost split sequences

Abstract

A major part of Iyama’s characterization of Auslander-Reiten quivers of representation-finite orders consists of an induction via rejective subcategories of ¤-lattices, which amounts to a resolution of ¤ as an isolated singularity. Despite of its useful applications (proof of Solomon’s second conjecture and the finiteness of representation dimension of any artinian al- gebra), rejective induction cannot be generalized to higher dimen- sional Cohen-Macaulay orders ¤. Our previous characterization of finite Auslander-Reiten quivers of ¤ in terms of additive func- tions [22] was proved by means of L-functors, but we still had to rely on rejective induction. In the present article, this dependence will be eliminated.