Abstract
ABSTRACTLet 𝒟 be a Krull–Schmidt, Hom-finite triangulated category with a Serre functor and a cluster-tilting object T. We introduce the notion of an FΛ-stable support τ-tilting module, induced by the shift functor and the Auslander–Reiten translation, in the cluster-tilted algebra . We show that there exists a bijection between basic cluster-tilting objects in 𝒟 and basic FΛ-stable support τ-tilting Λ-modules. This generalizes a result of Adachi–Iyama–Reiten [1]. As a consequence, we obtain that all cluster-tilting objects in 𝒟 have the same number of nonisomorphic indecomposable direct summands.
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