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arXiv · 2512.06160

Minimal varieties of algebras with graded involution and quadratic growth

Wesley Quaresma Cota·Ana Cristina Vieira
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Abstract

Subalgebras of upper triangular matrix algebras have played a fundamental role in the classification of minimal varieties of polynomial growth. Such classification has become a source of study in recent years since it leads to the more general classification of varieties of polynomial growth $n^k$, as has already been proven in many contexts for several values of $k$. In this paper, we study the asymptotic behavior of the sequence of codimensions of algebras graded by a finite group $G$ and endowed with a graded involution $*$, also called $(G,*)$-algebras. We classify the minimal varieties generated by a finite-dimensional $(G,*)$-algebra with quadratic growth.

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Wesley Quaresma Cota, Ana Cristina Vieira. 2025-12-05. Minimal varieties of algebras with graded involution and quadratic growth. https://arxiv.org/abs/2512.06160

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