2026/07/22 by Qi Bin, Yifu Han, Wei Hu
#math.RT #math.CO
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.