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PreprintCC BY-SA 4.0arXiv

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 𝔽 be a finite field. In this paper, we determine bases for the TG-ideals of graded polynomial identities of the algebra M2(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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Cite

BibTeXRIS
BibTeX
@misc{diniz2026graded,
  title = {{Graded identities for matrix algebras of order two over a finite field}},
  author = {Diogo Diniz and Eduardo Pinto da Fonsêca and Luis Filipe Ramos},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2605.30494},
  eprint = {2605.30494},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2605.30494},
  note = {CC BY-SA 4.0},
}
RIS
TY  - UNPB
TI  - Graded identities for matrix algebras of order two over a finite field
AU  - Diogo Diniz
AU  - Eduardo Pinto da Fonsêca
AU  - Luis Filipe Ramos
PY  - 2026
DA  - 2026/10/04
PB  - arXiv
DO  - 10.48550/arxiv.2605.30494
UR  - https://arxiv.org/abs/2605.30494
AB  - Let G be an arbitrary group and let 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(𝔽) for all possible G-gradings. The bases obtained consist of finitely many non-trivial graded identities, and are finite whenever G is finite.
ER  -