Blocks with quaternion defect group over a 2-adic ring: the case \tilde{A}

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/106109Except 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 a p-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 field k of characteristic 2 is Morita equivalent to $k\tilde A_4$. The main ingredients are Erdmann's classification of tame blocks and work of Cabanes and Picaronny on perfect isometries between tame blocks.18 pagesRepresentation TheoryGroup Theory20C05; 20C11;16G60Blocks with quaternion defect group over a 2-adic ring: the case \tilde{A}_4text