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Algebra and Discrete Mathematics, 2004, выпуск 1, страницы 87–111
(Mi adm330)
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Эта публикация цитируется в 2 научных статьях (всего в 2 статьях)
RESEARCH ARTICLE
Categories of lattices, and their global structure in terms of almost split sequences
Wolfgang Rump Institut für Algebra und
Zahlentheorie, Universität Stuttgart, Pfaffenwaldring 57, D–70550 Stuttgart, Germany
Аннотация:
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.
Ключевые слова:
L-functor, lattice category, $\tau$-category, Auslander-Reiten quiver.
Поступила в редакцию: 16.10.2003 Исправленный вариант: 26.01.2004
Образец цитирования:
Wolfgang Rump, “Categories of lattices, and their global structure in terms of almost split sequences”, Algebra Discrete Math., 2004, no. 1, 87–111
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/adm330 https://www.mathnet.ru/rus/adm/y2004/i1/p87
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