Minimal varieties of algebras with graded involution and quadratic growth
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866917129192734720 |
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| author | Cota, Wesley Quaresma Vieira, Ana Cristina |
| author_facet | Cota, Wesley Quaresma Vieira, Ana Cristina |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_06160 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Minimal varieties of algebras with graded involution and quadratic growth Cota, Wesley Quaresma Vieira, Ana Cristina Rings and Algebras Primary 16R10, 16R50, Secondary 16W10, 16W50 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. |
| title | Minimal varieties of algebras with graded involution and quadratic growth |
| topic | Rings and Algebras Primary 16R10, 16R50, Secondary 16W10, 16W50 |
| url | https://arxiv.org/abs/2512.06160 |