Blocks with a quaternion defect group over a 2-adic ring: the case Ã4

Thorsten Holm, Radha Kessar, Markus Linckelmann

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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 languageEnglish
Pages (from-to)29-43
Number of pages15
JournalGlasgow Mathematical Journal
Issue number1
Publication statusPublished - 1 Jan 2007

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