Lattices of t‐structures and thick subcategories for discrete cluster categories

Abstract

We classify t-structures and thick subcategories in any discrete cluster category C(Z) of Dynkin type 𝐴, and show that the set of all t-structures on C(Z) is a lattice under inclusion of aisles, with meet given by their intersection.We show that both the lattice of t-structures on C(Z) obtained in this way and the lattice of thick subcategories of C(Z) are intimately related to the lattice of non-crossing partitions of type 𝐴. In particular, the lattice of equivalence classes of non-degenerate tstructures on such a category is isomorphic to the lattice of non-crossing partitions of a finite linearly ordered set.