### 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 |
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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

*Glasgow Mathematical Journal*,

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

**Blocks with a quaternion defect group over a 2-adic ring : the case Ã4.** / Holm, Thorsten; Kessar, Radha; Linckelmann, Markus.

Research output: Contribution to journal › Article

*Glasgow Mathematical Journal*, vol. 49, no. 1, pp. 29-43. https://doi.org/10.1017/S0017089507003394

}

TY - JOUR

T1 - Blocks with a quaternion defect group over a 2-adic ring

T2 - the case Ã4

AU - Holm, Thorsten

AU - Kessar, Radha

AU - Linckelmann, Markus

PY - 2007/1/1

Y1 - 2007/1/1

N2 - 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.

AB - 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.

U2 - 10.1017/S0017089507003394

DO - 10.1017/S0017089507003394

M3 - Article

VL - 49

SP - 29

EP - 43

JO - Glasgow Mathematical Journal

JF - Glasgow Mathematical Journal

SN - 0017-0895

IS - 1

ER -