Codimensions of algebras with pseudoautomorphism and their exponential growth
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866912555611455488 |
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| author | Campedel, Elena Giordani, Ginevra Ioppolo, Antonio |
| author_facet | Campedel, Elena Giordani, Ginevra Ioppolo, Antonio |
| contents | Let $F$ be a fixed field of characteristic zero containing an element $i$ such that $i^2 = -1$. In this paper we consider finite dimensional superalgebras over $F$ endowed with a pseudoautomorphism $p$ and we investigate the asymptotic behaviour of the corresponding sequence of $p$-codimensions $c_n^p(A),$ $n=1,2, \ldots$. First we give a positive answer to a conjecture of Amitsur in this setting: the $p$-exponent $\exp^p(A) = \lim_{n \rightarrow \infty} \sqrt[n]{c_n^p(A)} $ always exists and it is an integer. In the final part we characterize the algebras whose exponential growth is bounded by $2$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_20898 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Codimensions of algebras with pseudoautomorphism and their exponential growth Campedel, Elena Giordani, Ginevra Ioppolo, Antonio Rings and Algebras 16R10, 16R50 (Primary) 16W10, 16W50 (Secondary) Let $F$ be a fixed field of characteristic zero containing an element $i$ such that $i^2 = -1$. In this paper we consider finite dimensional superalgebras over $F$ endowed with a pseudoautomorphism $p$ and we investigate the asymptotic behaviour of the corresponding sequence of $p$-codimensions $c_n^p(A),$ $n=1,2, \ldots$. First we give a positive answer to a conjecture of Amitsur in this setting: the $p$-exponent $\exp^p(A) = \lim_{n \rightarrow \infty} \sqrt[n]{c_n^p(A)} $ always exists and it is an integer. In the final part we characterize the algebras whose exponential growth is bounded by $2$. |
| title | Codimensions of algebras with pseudoautomorphism and their exponential growth |
| topic | Rings and Algebras 16R10, 16R50 (Primary) 16W10, 16W50 (Secondary) |
| url | https://arxiv.org/abs/2405.20898 |