BLOCKS WITH A QUATERNION DEFECT GROUP OVER A 2-ADIC RING: THE CASEÃ4

Abstract

Abstract.Except for blocks with a cyclic or Klein four defect group, it is not known in general whether the Morita equivalence class of a block algebra over a field of prime characteristic determines that of the corresponding block algebra over ap-adic ring. We prove this to be the case when the defect group is quaternion of order 8 and the block algebra over an algebraically closed fieldkof characteristic 2 is Morita equivalent tokÃ4. The main ingredients are Erdmann's classification of tame blocks [6] and work of Cabanes and Picaronny [4, 5] on perfect isometries between tame blocks.