Almost complete cluster tilting objects in generalized higher cluster categories

Details Almost complete cluster tilting objects in generalized higher cluster categories Almost complete cluster tilting objects in generalized higher cluster categories

2012-01-09

arxiv.org/abs/1201.1822v1

Mathematics

Representation Theory

26pages

Scientific paper

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.

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