Endomorphism rings of maximal rigid objects in cluster tubes

Details Endomorphism rings of maximal rigid objects in cluster tubes Endomorphism rings of maximal rigid objects in cluster tubes

2009-05-12

arxiv.org/abs/0905.1796v1

Mathematics

Representation Theory

Scientific paper

We describe the endomorphism rings of maximal rigid objects in the cluster
categories of tubes. Moreover, we show that they are gentle and have Gorenstein
dimension 1. We analyse their representation theory and prove that they are of
finite type. Finally, we study the relationship between the module category and
the cluster tube via the Hom-functor.

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