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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| Дата: | 2004 |
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| Формат: | Стаття |
| Мова: | English |
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Інститут прикладної математики і механіки НАН України
2004
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| Назва видання: | Algebra and Discrete Mathematics |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/155952 |
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| 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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irk-123456789-1559522019-06-18T01:30:39Z Categories of lattices, and their global structure in terms of almost split sequences Rump, W. 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. 2004 Article 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. http://dspace.nbuv.gov.ua/handle/123456789/155952 en Algebra and Discrete Mathematics Інститут прикладної математики і механіки НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Rump, W. |
| spellingShingle |
Rump, W. Categories of lattices, and their global structure in terms of almost split sequences Algebra and Discrete Mathematics |
| author_facet |
Rump, W. |
| author_sort |
Rump, W. |
| 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 |
| publisher |
Інститут прикладної математики і механіки НАН України |
| publishDate |
2004 |
| url |
http://dspace.nbuv.gov.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. |
| series |
Algebra and Discrete Mathematics |
| work_keys_str_mv |
AT rumpw categoriesoflatticesandtheirglobalstructureintermsofalmostsplitsequences |
| first_indexed |
2023-05-20T17:48:36Z |
| last_indexed |
2023-05-20T17:48:36Z |
| _version_ |
1796154138065633280 |