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Preprint Number 2581
2581. Vincent Bagayoko, Sebastian Krapp, Salma Kuhlmann, Daniel Panazzolo, Michele Serra Automorphisms and derivations on algebras endowed with formal infinite sums E-mail: Submission date: 9 March 2024 Abstract: 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. Mathematics Subject Classification: Keywords and phrases: |
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