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arXiv · 2512.06153

Group graded algebras and varieties with quadratic codimension growth

Wesley Quaresma Cota
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Abstract

Let $A$ be an associative algebra graded by a finite group $G$ over a field ${F}$ of characteristic zero. One associates to $A$ the sequence of $G$-graded codimensions $c_n^G(A)$, $n=1,2,\ldots$, which measures the growth of the polynomial identities satisfied by $A$. It is known that this sequence is either polynomially bounded or grows exponentially. In this paper, we study unitary $G$-graded varieties of polynomial codimension growth. In particular, we classify the varieties generated by unitary algebras with quadratic codimension growth and show that these varieties can be described as a direct sums of algebras that generate minimal $G$-graded varieties.

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Wesley Quaresma Cota. 2025-12-05. Group graded algebras and varieties with quadratic codimension growth. https://arxiv.org/abs/2512.06153

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