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 \(\Lambda\) consists of an induction via rejective subcategories of \(\Lambda\)-lattices, which amounts to a resolution of \(\Lambda\) as an isolated singularity. Despite of its useful applicati...
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Lugansk National Taras Shevchenko University
2018
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admjournalluguniveduua-article-9822018-05-14T08:03:48Z Categories of lattices, and their global structure in terms of almost split sequences Rump, Wolfgang \(L\)-functor, lattice category, \(\tau\) -category, Auslander-Reiten quiver 16G30, 16G70, 18E10; 16G60 A major part of Iyama's characterization of Auslander-Reiten quivers of representation-finite orders \(\Lambda\) consists of an induction via rejective subcategories of \(\Lambda\)-lattices, which amounts to a resolution of \(\Lambda\) 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 \(\Lambda\). Our previous characterization of finite Auslander-Reiten quivers of \(\Lambda\) 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. Lugansk National Taras Shevchenko University 2018-05-14 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/982 Algebra and Discrete Mathematics; Vol 3, No 1 (2004) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/982/511 Copyright (c) 2018 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
| baseUrl_str |
|
| datestamp_date |
2018-05-14T08:03:48Z |
| collection |
OJS |
| language |
English |
| topic |
\(L\)-functor lattice category \(\tau\) -category Auslander-Reiten quiver 16G30 16G70 18E10; 16G60 |
| spellingShingle |
\(L\)-functor lattice category \(\tau\) -category Auslander-Reiten quiver 16G30 16G70 18E10; 16G60 Rump, Wolfgang Categories of lattices, and their global structure in terms of almost split sequences |
| topic_facet |
\(L\)-functor lattice category \(\tau\) -category Auslander-Reiten quiver 16G30 16G70 18E10; 16G60 |
| format |
Article |
| author |
Rump, Wolfgang |
| author_facet |
Rump, Wolfgang |
| author_sort |
Rump, Wolfgang |
| title |
Categories of lattices, and their global structure in terms of almost split sequences |
| 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 |
| description |
A major part of Iyama's characterization of Auslander-Reiten quivers of representation-finite orders \(\Lambda\) consists of an induction via rejective subcategories of \(\Lambda\)-lattices, which amounts to a resolution of \(\Lambda\) 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 \(\Lambda\). Our previous characterization of finite Auslander-Reiten quivers of \(\Lambda\) 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. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2018 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/982 |
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AT rumpwolfgang categoriesoflatticesandtheirglobalstructureintermsofalmostsplitsequences |
| first_indexed |
2025-12-02T15:37:55Z |
| last_indexed |
2025-12-02T15:37:55Z |
| _version_ |
1850411451030700032 |