Automorphisms and derivations on algebras endowed with formal infinite sums

2024/03/09 by Vincent Bagayoko, Lothar Sebastian Krapp, Bagayoko, Vincent +7 · 3 citations
Computer Science · Mathematics · #Advanced Algebra and Logic #Advanced Topics in Algebra #FOS: Mathematics #Logic (math.LO) #Rings and Algebras (math.RA) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2403.05827

openalex publication_date 2024/03/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• Decomposing the Automorphism group of the surreal numbers
• Taylor expansions over generalised power series
• Algebraization of infinite summation

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