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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm123-1-6,
author = {Dagfinn F. Vatne},
title = {Endomorphism rings of maximal rigid objects in cluster tubes},
journal = {Colloquium Mathematicae},
volume = {122},
year = {2011},
pages = {63-93},
zbl = {1253.16017},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm123-1-6}
}
Dagfinn F. Vatne. Endomorphism rings of maximal rigid objects in cluster tubes. Colloquium Mathematicae, Tome 122 (2011) pp. 63-93. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm123-1-6/