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arXiv · 2405.05230

On $\operatorname{Alt}(n)$-modules with an additive dimension when $n\le6$

Barry Chin·Adrien Deloro·Joshua Wiscons·Andy Yu
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Abstract

Working in the general context of "modules with an additive dimension," we complete the determination of the minimal dimension of a faithful Alt(n)-module and classify those modules in three of the exceptional cases: 2-dimensional Alt(5)-modules in characteristic 2, 3-dimensional Alt(5)-modules in characteristic 5, and 3-dimensional Alt(6)-modules in characteristic 3. We also highlight the remaining work needed to complete the classification of the faithful Alt(n)-modules of minimal dimension for all n; these open problems seem well suited as projects for advanced undergraduate or master's students.

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Barry Chin, Adrien Deloro, Joshua Wiscons, Andy Yu. 2024-05-08. On $\operatorname{Alt}(n)$-modules with an additive dimension when $n\le6$. https://doi.org/10.2140/involve.2026.19.311

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