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arXiv · 2512.06164

On the colength sequence of algebras with graded involution

Wesley Quaresma Cota·Rafael Bezerra dos Santos·Ana Cristina Vieira
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Abstract

In recent years, many results have been established regarding classifications of varieties whose colength sequences are bounded by a fixed constant. In this work, we explore this theme in the setting of algebras endowed with a graded involution, called $(G,*)$-algebras. We give an explicit description of the decomposition of the $\langle n \rangle$-cocharacter for some important $(G,*)$-algebras $A$, for every $\langle n \rangle=(n_1, \ldots, n_{2t})$. For each algebra $A$, the $n$th colength is defined as the number of irreducible components that appear in these decompositions. Our aim is to classify varieties whose $n$th colengths are bounded by a fixed constant.

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Wesley Quaresma Cota, Rafael Bezerra dos Santos, Ana Cristina Vieira. 2025-12-05. On the colength sequence of algebras with graded involution. https://arxiv.org/abs/2512.06164

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