AI 中文总结
本文在2-模系统下构造了$\mathcal{O}{\rm SU}_3(2)$的块代数$B$，其与$\mathcal{O} Q_8$森田等价但非整体同型，进而得出二者非$p$-置换等价与精彩Rickard等价的结论。
AI 中文摘要
设$(K,\mathcal{O},k)$为足够大的2-模系统，本文证明$\mathcal{O}{\rm SU}_3(2)$的块代数$B$与$\mathcal{O} Q_8$通过具有3维内平凡源的双模森田等价；还证明$B$与$\mathcal{O} Q_8$非整体同型，故二者非$p$-置换等价也非精彩Rickard等价。
英文摘要
Let $(K,\mathcal{O},k)$ be a large enough $2$-modular system. We show that there is a block algebra $B$ of $\mathcal{O}{\rm SU}_3(2)$ which is Morita equivalent to $\mathcal{O} Q_8$ via a bimodule with a $3$-dimensional endotrivial source. We also prove that $B$ and $\mathcal{O} Q_8$ are not globally isotypic. Hence they are not $p$-permutation equivalent and not splendidly Rickard equivalent.
