2-adic环上具有四元数亏群的块：\tilde{A}_4情形
Blocks with quaternion defect group over a 2-adic ring: the case \tilde{A}_4
摘要：
除了具有循环亏群或Klein四亏群的块之外，一般不知道素特征域上的块代数的Morita等价类是否决定了p-adic环上相应块代数的Morita等价类.我们证明了这是当缺陷群是8阶四元数和块代数特征为2的代数闭域k是森田等价于$k\tilde A_4$的情况下。主要成分是Erdmann的驯服块的分类和Cabanes和Picaronny的驯服块之间的完美等距的工作。
英文摘要：
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.
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