Quadratic codimension growth and minimal varieties of unitary algebras with superinvolution
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
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2026
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| _version_ | 1866908761360171008 |
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| author | Cota, Wesley Quaresma Matos, Luiz Henrique de Souza |
| author_facet | Cota, Wesley Quaresma Matos, Luiz Henrique de Souza |
| contents | Let $A$ be an associative algebra with a superinvolution $*$ over a field of characteristic zero, and let $c_n^*(A)$, $n = 1, 2, \ldots$, denote its sequence of $*$-codimensions. It is well known that this sequence is either polynomially bounded or grows exponentially. In the polynomial case, a central problem in PI-theory is the classification of varieties ${V}$ for which $c_n^*({V}) \approx αn^k$ for a given $k$. One of the main objectives of this paper is to classify minimal varieties of unitary algebras endowed with a superinvolution that exhibit quadratic codimension growth. We obtain a structural characterization, up to PI-equivalence, of all unitary algebras with quadratic codimension growth. As a consequence, we show that any unitary variety of quadratic codimension growth is generated by a direct sum of algebras generating minimal varieties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_08092 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Quadratic codimension growth and minimal varieties of unitary algebras with superinvolution Cota, Wesley Quaresma Matos, Luiz Henrique de Souza Rings and Algebras Primary 16R10, 16W50, Secondary 20C30, 16W55 Let $A$ be an associative algebra with a superinvolution $*$ over a field of characteristic zero, and let $c_n^*(A)$, $n = 1, 2, \ldots$, denote its sequence of $*$-codimensions. It is well known that this sequence is either polynomially bounded or grows exponentially. In the polynomial case, a central problem in PI-theory is the classification of varieties ${V}$ for which $c_n^*({V}) \approx αn^k$ for a given $k$. One of the main objectives of this paper is to classify minimal varieties of unitary algebras endowed with a superinvolution that exhibit quadratic codimension growth. We obtain a structural characterization, up to PI-equivalence, of all unitary algebras with quadratic codimension growth. As a consequence, we show that any unitary variety of quadratic codimension growth is generated by a direct sum of algebras generating minimal varieties. |
| title | Quadratic codimension growth and minimal varieties of unitary algebras with superinvolution |
| topic | Rings and Algebras Primary 16R10, 16W50, Secondary 20C30, 16W55 |
| url | https://arxiv.org/abs/2601.08092 |