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The Image of the Derived Category in the Cluster Category

2012
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International mathematics research notices
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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 the more general setup of algebras of global dimension at most 2, cluster categories are defined to be these triangulated hulls of the orbit categories. In this paper we study the image of the natural functor

doi:10.1093/imrn/rns010
fatcat:usnvn27cobbs3pw635ompibewm