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

Wesley Quaresma Cota; Daniela Martinez Correa

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arXiv · 2610.17408

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 $D=F(e_{11}+e_{33})+Fe_{22}+Fe_{12}+Fe_{13}+Fe_{23} \subseteq UT_3$ and $D_0=Fe_{22}+Fe_{33}+Fe_{12}+Fe_{13}+Fe_{14}+Fe_{23}+Fe_{24}+Fe_{34} \subseteq UT_4$ 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 $\mathbb{Z}_2$-gradings.

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BibTeX RIS

Wesley Quaresma Cota, Daniela Martinez Correa. 2026-10-12. Group gradings, graded identities and central polynomials of algebras with almost polynomial $δ$-growth. https://arxiv.org/abs/2610.17408

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