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

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 applicat...

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Veröffentlicht in:Algebra and Discrete Mathematics
Datum:2004
1. Verfasser: Rump, W.
Format: Artikel
Sprache:Englisch
Veröffentlicht: Інститут прикладної математики і механіки НАН України 2004
Online Zugang:https://nasplib.isofts.kiev.ua/handle/123456789/155952
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Zitieren: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.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
Beschreibung
Zusammenfassung: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.
ISSN:1726-3255