On the colength sequence of algebras with graded involution
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866909946763804672 |
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| author | Cota, Wesley Quaresma Santos, Rafael Bezerra dos Vieira, Ana Cristina |
| author_facet | Cota, Wesley Quaresma Santos, Rafael Bezerra dos Vieira, Ana Cristina |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_06164 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the colength sequence of algebras with graded involution Cota, Wesley Quaresma Santos, Rafael Bezerra dos Vieira, Ana Cristina Rings and Algebras Primary 16R10, 16R50, Secondary 16W10, 16W50, 20C30 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. |
| title | On the colength sequence of algebras with graded involution |
| topic | Rings and Algebras Primary 16R10, 16R50, Secondary 16W10, 16W50, 20C30 |
| url | https://arxiv.org/abs/2512.06164 |