Acyclic Calabi-Yau categories are cluster categories
نویسنده
چکیده
Let k be a field and Q a finite quiver without oriented cycles. Let kQ be the path algebra of Q and mod kQ the category of k-finite-dimensional right kQ-modules. The cluster category CQ was introduced in [1] (for general Q) and, independently, in [4] (for Q of type An). It is defined as the orbit category of the bounded derived category D(mod kQ) under the action of the automorphism Σ−1 ◦ S, where S is the suspension (=shift) functor of the derived category and Σ its Serre functor, characterized by the Serre duality formula
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