Dimensions of finite type for representations of partially ordered sets

Abstract

We consider the dimensions of finite type of rep- resentations of a partially ordered set, i.e. such that there is only finitely many isomorphism classes of representations of this dimen- sion. 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 di- mension of finite type. Moreover, if such a representation exists, it only has scalar endomorphisms. These results generalize those of