Almost Complete Cluster Tilting Objects in Generalized Higher Cluster Categories
نویسنده
چکیده
We study higher cluster tilting objects in generalized higher cluster categories arising from dg algebras of higher Calabi-Yau dimension. Taking advantage of silting mutations of Aihara-Iyama, we obtain a class of m-cluster tilting objects in generalized m-cluster categories. For generalized m-cluster categories arising from strongly (m + 2)-Calabi-Yau dg algebras, by using truncations of minimal cofibrant resolutions of simple modules, we prove that each almost complete mcluster tilting P -object has exactly m + 1 complements with periodicity property. This leads us to the conjecture that each liftable almost complete m-cluster tilting object has exactly m+1 complements in generalized m-cluster categories arising from m-rigid good completed deformed preprojective dg algebras.
منابع مشابه
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