Folded tilting complexes for Brauer tree algebras

We give dual one-sided tilting complexes producing inverse equivalences of the derived category of a Brauer star algebra and a Brauer tree algebra of the same type, folded according to an additional combinatorial structure on the Brauer tree. We relate this to the two-sided two-term tilting complex of Rouquier in the case of a group block, showing that it induces the "completely folded" case for each one-sided complex.