This article is cited in 1 paper

RESEARCH ARTICLE

Dimensions of finite type for representations of partially ordered sets

Yuriy A. Drozd, Eugene A. Kubichka

Department of Mechanics and Mathematics, Kyiv Taras Shevchenko University, 01033 Kyiv, Ukraine

Abstract: 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].

Keywords: Representations of posets, finite type, indecomposable representations.

MSC: 16G20,16G60

Language: English

Bibliographic databases:

• 
•