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

Involve a Journal of Mathematics 2026 Open access

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Authors: Barry Chin, Adrien Deloro, Joshua Wiscons, Andy S. Yu
DOI: 10.2140/involve.2026.19.311
Cited by: 0
References: 7

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.

Fields of Study & Subjects

Rings Modules and Algebras Holomorphic and Operator Theory Commutative Algebra and Its Applications

Publication details

Journal / source
Involve a Journal of Mathematics
Volume
19
Issue
2
Pages
311–336
Publication date
8 March 2026
Language
EN