On Alt(n)-modules with an additive dimension when n ≤ 6

Chin, Barry; Deloro, Adrien; Wiscons, Joshua; Yu, Andy

doi:10.2140/involve.2026.19.311

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

Barry Chin, Adrien Deloro, Joshua Wiscons and Andy Yu

Vol. 19 (2026), No. 2, 311–336

DOI: 10.2140/involve.2026.19.311

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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Keywords

alternating group, finite-dimensional algebra, first-order representation theory

Mathematical Subject Classification

Primary: 20C30

Secondary: 03C60, 20F11

Milestones

Received: 8 May 2024

Revised: 26 August 2024

Accepted: 29 October 2024

Published: 8 March 2026

Communicated by Vadim Ponomarenko

Authors

Barry Chin
Department of Mathematics Cal Poly Humboldt Arcata, CA United States

Adrien Deloro
Institut de Mathématiques de Jussieu Sorbonne Université Paris France

Joshua Wiscons
Department of Mathematics and Statistics California State University Sacramento, CA United States

Andy Yu
Monterey Trail High School Elk Grove, CA United States

Vol. 19, No. 2, 2026