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PreprintarXiv licencearXiv

Identities and isomorphisms of finite graded matrix algebras

  • Diogo Diniz
  • Daniela Martinez Correa
  • Dimas José Gonçalves
  • Plamen Koshlukov
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Abstract

Let 𝔽 be a finite field and let G be a group such that every finite subgroup of G is cyclic. In this paper we classify the division gradings by cyclic groups on matrix algebras over 𝔽. This yields the classification of the G-gradings on these algebras. Moreover if G is abelian we prove that two matrix algebras over 𝔽 with G-gradings satisfy the same graded identities if and only if they are isomorphic as graded algebras.

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Cite

BibTeXRIS
BibTeX
@misc{diniz2026identities,
  title = {{Identities and isomorphisms of finite graded matrix algebras}},
  author = {Diogo Diniz and Daniela Martinez Correa and Dimas José Gonçalves and Plamen Koshlukov},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.20113},
  eprint = {2610.20113},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.20113},
}
RIS
TY  - UNPB
TI  - Identities and isomorphisms of finite graded matrix algebras
AU  - Diogo Diniz
AU  - Daniela Martinez Correa
AU  - Dimas José Gonçalves
AU  - Plamen Koshlukov
PY  - 2026
DA  - 2026/10/14
PB  - arXiv
DO  - 10.48550/arxiv.2610.20113
UR  - https://arxiv.org/abs/2610.20113
AB  - Let 𝔽 be a finite field and let G be a group such that every finite subgroup of G is cyclic. In this paper we classify the division gradings by cyclic groups on matrix algebras over 𝔽. This yields the classification of the G-gradings on these algebras. Moreover if G is abelian we prove that two matrix algebras over 𝔽 with G-gradings satisfy the same graded identities if and only if they are isomorphic as graded algebras.
ER  -