Cluster tilting objects in generalized higher cluster categories

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.

27 pages

References in corpus (4)

• On triangulated orbit categories
• Calabi-Yau algebras
• Acyclic Calabi-Yau categories
• Deformed Calabi-Yau Completions