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arXiv · 1005.3564

Cluster tilting objects in generalized higher cluster categories

Lingyan Guo
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Abstract

We prove the existence of an $m$-cluster tilting object in a generalized $m$-cluster category which is $(m+1)$-Calabi-Yau and Hom-finite, arising from an $(m+2)$-Calabi-Yau dg algebra. This is a generalization of the result for the ${m = 1}$ case in Amiot's Ph.~D.~thesis. Our results apply in particular to higher cluster categories associated to suitable finite-dimensional algebras of finite global dimension, and higher cluster categories associated to Ginzburg dg categories coming from suitable graded quivers with superpotential.

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Lingyan Guo. 2010-06-08. Cluster tilting objects in generalized higher cluster categories. https://arxiv.org/abs/1005.3564

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