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• W1921856609 abstract "Assume that $mathcal{D}$ is a Krull-Schmidt, Hom-finite triangulated category with a Serre functor and a cluster-tilting object $T$. We introduce the notion of ghost-tilting objects, and $T[1]$-tilting objects in $mathcal{D}$, which are a generalization of cluster-tilting objects. When $mathcal{D}$ is $2$-Calabi-Yau, the ghost-tilting objects are cluster-tilting. Let $Lambda={rm End}^{op}_{mathcal{D}}(T)$ be the endomorphism algebra of $T$. We show that there exists a bijection between $T[1]$-tilting objects in $mathcal{D}$ and support $tau$-tilting $Lambda$-modules, which generalizes a result of Adachi-Iyama-Reiten [AIR]. We develop a basic theory on $T[1]$-tilting objects. In particular, we introduce a partial order on the set of $T[1]$-tilting objects and mutation of $T[1]$-tilting objects, which can be regarded as a generalization of `cluster-tilting mutation'. As an application, we give a partial answer to a question posed in [AIR]." @default.
• W1921856609 created "2016-06-24" @default.
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• W1921856609 date "2015-04-01" @default.
• W1921856609 modified "2023-09-27" @default.
• W1921856609 title "Ghost-tilting objects in triangulated categories" @default.
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