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arXiv · 2605.30494

Graded identities for matrix algebras of order two over a finite field

Diogo Diniz·Eduardo Pinto da Fonsêca·Luis Filipe Ramos
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Abstract

Let $G$ be an arbitrary group and let $\mathbb{F}$ be a finite field. In this paper, we determine bases for the $T_G$-ideals of graded polynomial identities of the algebra $M_2(\mathbb{F})$ for all possible $G$-gradings. The bases obtained consist of finitely many non-trivial graded identities, and are finite whenever $G$ is finite.

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Diogo Diniz, Eduardo Pinto da Fonsêca, Luis Filipe Ramos. 2026-05-28. Graded identities for matrix algebras of order two over a finite field. https://arxiv.org/abs/2605.30494

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