Graded Blocks of Group Algebras

We introduce the idea of transfer of gradings via derived equivalences and we apply it to construct positive gradings on a basic

Brauer tree algebra corresponding to an arbitrary Brauer tree T. We do this by transferring gradings via derived equivalence from a basic Brauer tree algebra, whose tree is a star. To transfer gradings via derived equivalence we use tilting

complexes constructed by taking Green's walk around T. We also prove that there is a unique grading on an arbitrary Brauer tree algebra, up to graded Morita equivalence and rescaling.