### 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 kÃ44. 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.

Original language | English |
---|---|

Pages (from-to) | 29-43 |

Number of pages | 15 |

Journal | Glasgow Mathematical Journal |

Volume | 49 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1 Jan 2007 |

## Cite this

Holm, T., Kessar, R., & Linckelmann, M. (2007). Blocks with a quaternion defect group over a 2-adic ring: the case Ã4.

*Glasgow Mathematical Journal*,*49*(1), 29-43. https://doi.org/10.1017/S0017089507003394