Graded algebras with homogeneous involution and varieties of almost polynomial growth

Wesley Quaresma Cota; Felipe Yasumura

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arXiv · 2512.04769

Graded algebras with homogeneous involution and varieties of almost polynomial growth

Wesley Quaresma Cota·Felipe Yasumura

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Abstract

An important aspect in the theory of algebras with polynomial identities is the study of the asymptotic behavior of the codimension sequence $c_n(A),\, n\geq 1,$ which measures the growth of polynomial identities of a given algebra $A$. In this context, graded identities naturally arise as prominent tools, since ordinary polynomial identities can be viewed as a particular case of graded identities. Moreover, as an involution does not necessarily preserve the homogeneous components of a grading, it is natural to consider the notion of a homogeneous involution. In this work, we investigate the behavior of the codimension sequence in the setting of $G$-graded algebras endowed with a homogeneous involution. More specifically, we characterize the varieties of polynomial growth in terms of the exclusion of a list of algebras from the variety. As a consequence, we provide the classification of the varieties with almost polynomial growth in this setting.

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Wesley Quaresma Cota, Felipe Yasumura. 2025-12-04. Graded algebras with homogeneous involution and varieties of almost polynomial growth. https://arxiv.org/abs/2512.04769

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