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Relative cluster categories

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 نشر من قبل Yilin Wu
 تاريخ النشر 2021
  مجال البحث
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 تأليف Yilin Wu




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We generalize the construction of (higher) cluster categories by Claire Amiot and by Lingyan Guo to the relative context. We prove the existence of an $ n $-cluster tilting object in a Frobenius extriangulated category which is stably $ n $-Calabi--Yau and Hom-finite, arising from a left $ (n+1) $-Calabi--Yau morphism. Our results apply in particular to relative Ginzburg dg algebras coming from ice quivers with potential and higher Auslander algebras associated to $ n $-representation-finite algebras.



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