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PreprintCC BY 4.0arXiv

Group gradings, graded identities and central polynomials of algebras with almost polynomial δ-growth

  • Wesley Quaresma Cota
  • Daniela Martinez Correa
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Abstract

The finite-dimensional F-algebras D=F(e11+e33)+Fe22+Fe12+Fe13+Fe23 ⊆ UT3 and D0=Fe22+Fe33+Fe12+Fe13+Fe14+Fe23+Fe24+Fe34 ⊆ UT4 occupy a distinguished position in the theory of central polynomials. Together with the infinite-dimensional Grassmann algebra, these algebras generate the only varieties of almost polynomial growth of proper central codimensions. We determine finite generating sets for their T-spaces of central polynomials and compute their central and proper central codimensions. We also prove that every group grading on D0 is isomorphic to an elementary grading and determine the identities and codimensions associated with all its ℤ2-gradings.

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Cite

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BibTeX
@misc{cota2026group,
  title = {{Group gradings, graded identities and central polynomials of algebras with almost polynomial $δ$-growth}},
  author = {Wesley Quaresma Cota and Daniela Martinez Correa},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.17408},
  eprint = {2610.17408},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.17408},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Group gradings, graded identities and central polynomials of algebras with almost polynomial δ-growth
AU  - Wesley Quaresma Cota
AU  - Daniela Martinez Correa
PY  - 2026
DA  - 2026/10/12
PB  - arXiv
DO  - 10.48550/arxiv.2610.17408
UR  - https://arxiv.org/abs/2610.17408
AB  - The finite-dimensional F-algebras D=F(e_11+e_33)+Fe_22+Fe_12+Fe_13+Fe_23 ⊆ UT_3 and D_0=Fe_22+Fe_33+Fe_12+Fe_13+Fe_14+Fe_23+Fe_24+Fe_34 ⊆ UT_4 occupy a distinguished position in the theory of central polynomials. Together with the infinite-dimensional Grassmann algebra, these algebras generate the only varieties of almost polynomial growth of proper central codimensions. We determine finite generating sets for their T-spaces of central polynomials and compute their central and proper central codimensions. We also prove that every group grading on D_0 is isomorphic to an elementary grading and determine the identities and codimensions associated with all its ℤ_2-gradings.
ER  -