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

Holm, T., Kessar, R. and Linckelmann, M. (2007). Blocks with quaternion defect group over a 2-adic ring: the case \tilde{A}_4. Glasgow Mathematical Journal, 49(1), pp. 29-43. doi: 10.1017/S0017089507003394

## 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 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.

Publication Type: Article 18 pages Q Science > QA Mathematics School of Mathematics, Computer Science & Engineering > Mathematics http://arxiv.org/abs/math/0512125v1 http://openaccess.city.ac.uk/id/eprint/1899
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