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 applications (proof of Solomon’s second...

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Veröffentlicht in:Algebra and Discrete Mathematics
Datum:2004
1. Verfasser: Rump, W.
Format: Artikel
Sprache:English
Veröffentlicht: Інститут прикладної математики і механіки НАН України 2004
Online Zugang:https://nasplib.isofts.kiev.ua/handle/123456789/155952
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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
id nasplib_isofts_kiev_ua-123456789-155952
record_format dspace
spelling Rump, W.
2019-06-17T15:48:26Z
2019-06-17T15:48:26Z
2004
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.
1726-3255
2000 Mathematics Subject Classification: 16G30, 16G70, 18E10; 16G60.
https://nasplib.isofts.kiev.ua/handle/123456789/155952
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.
en
Інститут прикладної математики і механіки НАН України
Algebra and Discrete Mathematics
Categories of lattices, and their global structure in terms of almost split sequences
Article
published earlier
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
title Categories of lattices, and their global structure in terms of almost split sequences
spellingShingle Categories of lattices, and their global structure in terms of almost split sequences
Rump, W.
title_short Categories of lattices, and their global structure in terms of almost split sequences
title_full Categories of lattices, and their global structure in terms of almost split sequences
title_fullStr Categories of lattices, and their global structure in terms of almost split sequences
title_full_unstemmed Categories of lattices, and their global structure in terms of almost split sequences
title_sort categories of lattices, and their global structure in terms of almost split sequences
author Rump, W.
author_facet Rump, W.
publishDate 2004
language English
container_title Algebra and Discrete Mathematics
publisher Інститут прикладної математики і механіки НАН України
format Article
description 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
url https://nasplib.isofts.kiev.ua/handle/123456789/155952
citation_txt 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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first_indexed 2025-12-07T19:57:25Z
last_indexed 2025-12-07T19:57:25Z
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