Automorphisms and derivations on algebras endowed with formal infinite sums
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arXiv
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| Auteurs principaux: | , , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866915505089019904 |
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| author | Bagayoko, Vincent Krapp, Lothar Sebastian Kuhlmann, Salma Panazzolo, Daniel Serra, Michele |
| author_facet | Bagayoko, Vincent Krapp, Lothar Sebastian Kuhlmann, Salma Panazzolo, Daniel Serra, Michele |
| contents | We establish a correspondence between automorphisms and derivations on certain algebras of generalised power series. In particular, we describe a Lie algebra of derivations on a field $k(\!(G)\!)$ of generalised power series, exploiting our knowledge of its group of valuation preserving automorphisms. The correspondence is given by the formal Taylor expansion of the exponential. In order to define the exponential map, we develop an appropriate notion of summability of infinite families in algebras. We show that there is a large class of algebras in which the exponential induces the above correspondence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_05827 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Automorphisms and derivations on algebras endowed with formal infinite sums Bagayoko, Vincent Krapp, Lothar Sebastian Kuhlmann, Salma Panazzolo, Daniel Serra, Michele Rings and Algebras Logic We establish a correspondence between automorphisms and derivations on certain algebras of generalised power series. In particular, we describe a Lie algebra of derivations on a field $k(\!(G)\!)$ of generalised power series, exploiting our knowledge of its group of valuation preserving automorphisms. The correspondence is given by the formal Taylor expansion of the exponential. In order to define the exponential map, we develop an appropriate notion of summability of infinite families in algebras. We show that there is a large class of algebras in which the exponential induces the above correspondence. |
| title | Automorphisms and derivations on algebras endowed with formal infinite sums |
| topic | Rings and Algebras Logic |
| url | https://arxiv.org/abs/2403.05827 |