Dimensions of finite type for representations of partially ordered sets

• Опубліковано в: : Algebra and Discrete Mathematics
• Дата: 2004
• Автори: Drozd, Y.A., Kubichka, E.A.
• Формат: Стаття
• Мова: English
• Опубліковано: Інститут прикладної математики і механіки НАН України 2004
• Онлайн доступ: https://nasplib.isofts.kiev.ua/handle/123456789/156411
• Назва журналу: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Цитувати: Dimensions of finite type for representations of partially ordered sets / Y.A. Drozd, E.A. Kubichka // Algebra and Discrete Mathematics. — 2004. — Vol. 3, № 3. — С. 21–37. — Бібліогр.: 13 назв. — англ.

We consider the dimensions of finite type of representations of a partially ordered set, i.e. such that there is only finitely many isomorphism classes of representations of this dimension. We give a criterion for a dimension to be of finite type. We also characterize those dimensions of finite type, for which there is an indecomposable representation of this dimension, and show that there can be at most one indecomposable representation of any dimension of finite type. Moreover, if such a representation exists, it only has scalar endomorphisms. These results (Theorem 1.6, page 25) generalize those of [5, 1, 9].