We study associative $G$-graded algebras with 1 of polynomial $G$-codimension growth, where $G$ is a finite group. For any fixed $k\geq 1,$ we construct associative $G$-graded algebras of upper triangular matrices whose $G$-codimension sequence is given asymptotically by a polynomial of degree $k$ whose leading coefficient is the largest or smallest possible.
La Mattina, D. (2009). Polynomial codimension growth of graded algebras. In Contemporary Mathematics (pp.189-198).
Polynomial codimension growth of graded algebras
LA MATTINA, Daniela
2009-01-01
Abstract
We study associative $G$-graded algebras with 1 of polynomial $G$-codimension growth, where $G$ is a finite group. For any fixed $k\geq 1,$ we construct associative $G$-graded algebras of upper triangular matrices whose $G$-codimension sequence is given asymptotically by a polynomial of degree $k$ whose leading coefficient is the largest or smallest possible.
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