0
2020.
GRADINGS ON QUATERNION BLOCKS WITH TWO SIMPLE MODULES
In this paper we show that tame blocks of group algebras with quaternion defect groups and two isomorphism classes of simple modules can be non-trivially graded. We prove this by using the transfer of gradings via derived equivalences. The gradings that we transfer are such that the arrows of the quiver are homogeneous elements. We also show that, up to graded Morita equivalence, on such a block there exists a unique grading.