特征3下的马蒂厄群${\sf M}_{12}$与${\mathbf{SL_3(3)}}$
The Mathieu group ${\sf M}_{12}$ vs ${\mathbf{SL_3(3)}}$ in characteristic 3
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中文总结 AI 辅助
研究特征3下马蒂厄群${\sf M}_{12}$与${\mathbf{SL_3(3)}}$，运用里卡德定理证明其主3 - 块出色里卡德等价及导出等价，还回答了W. 墨菲关于主3 - 块一阶霍赫希尔德上同调的问题。
中文摘要 AI 辅助
我们证明了马蒂厄群${\sf M_{12}}$和特殊线性群$\SL_3(3)$的主3 - 块是出色的里卡德等价的，因此是导出等价的。通过应用可追溯到第二作者的里卡德定理，作为副产品，我们回答了W. 墨菲提出的关于上述主3 - 块的一阶霍赫希尔德上同调的问题。
英文摘要
We prove that the principal $3$-blocks of the Mathieu group ${\sf M_{12}}$ and the special linear group $\SL_3(3)$ are splendidly Rickard equivalent, and hence derived equivalent, by applying Rickard's theorem whose origin goes back to the second author. As a byproduct we answer to a question on the first Hochschild cohomology of the principal $3$-blocks above posed by W. Murphy.
