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.
