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arXiv · 2607.19916

Higher cluster tilting objects in locally finite triangulated categories

Qi Bin·Yifu Han·Wei Hu
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Abstract

We study higher cluster tilting objects through covering functors from derived categories of hereditary algebras. The covering formalism reduces the existence problem to the equivariant problem of finding \(G\)-stable \(d\)-cluster tilting objects in \(d\)-cluster categories. For triangulated categories with finitely many indecomposable objects this gives a complete ADE existence criterion and explicit counting formulas. We also prove that, in finite Frobenius models, the endomorphism algebras of all \(d\)-cluster tilting objects are derived equivalent. Applications are given to Cohen--Macaulay finite categories, finite noncommutative crepant resolutions, and rigidity dimensions of representation-finite self-injective algebras.

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Qi Bin, Yifu Han, Wei Hu. 2026-07-22. Higher cluster tilting objects in locally finite triangulated categories. https://arxiv.org/abs/2607.19916

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