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

• Опубліковано в: : Algebra and Discrete Mathematics
• Дата: 2004
• Автор: Rump, W.
• Формат: Стаття
• Мова: Англійська
• Опубліковано: Інститут прикладної математики і механіки НАН України 2004
• Онлайн доступ: https://nasplib.isofts.kiev.ua/handle/123456789/155952
• Назва журналу: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Цитувати: Categories of lattices, and their global structure in terms of almost split sequences / W. Rump // Algebra and Discrete Mathematics. — 2004. — Vol. 3, № 1. — С. 87–111. — Бібліогр.: 30 назв. — англ.

A major part of Iyama’s characterization of
 Auslander-Reiten quivers of representation-finite orders Λ consists
 of an induction via rejective subcategories of Λ-lattices, which
 amounts to a resolution of Λ as an isolated singularity. Despite
 of its useful applications (proof of Solomon’s second conjecture
 and the finiteness of representation dimension of any artinian algebra), rejective induction cannot be generalized to higher dimensional Cohen-Macaulay orders Λ. Our previous characterization
 of finite Auslander-Reiten quivers of Λ in terms of additive functions [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.