In this paper the class of Brauer graph algebras is proved to be closed under derived equivalence. For that we use the rank of the maximal torus of the identity component Out0(A)of the group of outer automorphisms of a symmetric stably biserial algebra A .
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.
