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arXiv · 2607.15825

The Mathieu group ${\sf M}_{12}$ vs ${\mathbf{SL_3(3)}}$ in characteristic 3

Shigeo Koshitani·Tetsuro Okuyama
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Abstract

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.

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BibTeXRIS

Shigeo Koshitani, Tetsuro Okuyama. 2026-07-17. The Mathieu group ${\sf M}_{12}$ vs ${\mathbf{SL_3(3)}}$ in characteristic 3. https://arxiv.org/abs/2607.15825

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