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

Wesley Quaresma Cota; Daniela Martinez Correa

paper

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

arXiv:2610.17408

Abstract

The finite-dimensional $F$ -algebras $D = F (e_{11} + e_{33}) + F e_{22} + F e_{12} + F e_{13} + F e_{23} \subseteq U T_{3}$ and $D_{0} = F e_{22} + F e_{33} + F e_{12} + F e_{13} + F e_{14} + F e_{23} + F e_{24} + F e_{34} \subseteq U T_{4}$ 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.

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

Abstract

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