Claire Amiot, Steffen Oppermann
Published 2010-10-06Version 1
Cluster categories of hereditary algebras have been introduced as orbit categories of their derived categories. Keller has pointed out that for non-hereditary algebras orbit categories need not be triangulated, and he introduced the notion of triangulated hull to overcome this problem. In this paper we study the image if the natural functor from the bounded derived category to the cluster category, that is we investigate how far the orbit category is from being the cluster category. We show that for wide classes of non-piecewise hereditary algebras the orbit category is never equal to the cluster category.
Cluster categories of type $\mathbb{A}_\infty^\infty$ and triangulations of the infinite strip
A geometric description of $m$-cluster categories
A geometric realization of the $m$-cluster category of type $\tilde{A}$
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