Dimensions of finite type for representations of partially ordered sets

Details Dimensions of finite type for representations of partially ordered sets Dimensions of finite type for representations of partially ordered sets

2004-04-13

arxiv.org/abs/math/0404242v1

Algebra and Discrete Math. 3, No.3 (2004), 20-36

Mathematics

Representation Theory

14 pages

Scientific paper

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.

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