Almost complete cluster tilting objects in generalized higher cluster categories
By Lingyan Guo. 2010
53 citations recorded by the source corpus.
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 $m$-cluster 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.
Subfields: Algebra and Number Theory, Geometry and Topology, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/b70dc88fa7fbee38f4ca418c8f83a5d2707f144d
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Citations in the corpus
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