Blocks with quaternion defect group over a 2-adic ring: the case \tilde{A}_4

Holm, Thorsten; Kessar, Radha; Linckelmann, Markus

Blocks with quaternion defect group over a 2-adic ring: the case \tilde{A}_4

Authors

Holm, Thorsten

Kessar, Radha

Linckelmann, Markus

Description

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 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 pages