9 papers
A formal Lie correspondence
Vincent Bagayoko
We establish an equivalence between categories of 'formally nilpotent' Lie algebras and exponential groups in characteristic zero. It extends the equivalences of Mal'cev, Lazard, Q…
Automorphisms and derivations on algebras endowed with formal infinite sums
Vincent Bagayoko, Lothar Sebastian Krapp, Salma Kuhlmann +2
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 fi…
Groups with infinite linearly ordered products
Vincent Bagayoko
We introduce a formalism of infinite, linearly ordered products in general groups. Using this, we define infinite compositions in certain groups of formal power series such as tran…
Ordered groups of formal series, and a conjugacy problem
Vincent Bagayoko
Given an ordered field of formal series over an ordered field equipped with a composition law $\circ \colon \mathbb{T} \times \mathbb{T}^{>\mathbb{R}} \lo…
Taylor expansions over generalised power series
Vincent Bagayoko, Vincenzo Mantova
We study the existence of formal Taylor expansions for functions defined on fields of generalised series. We prove a general result for the existence and convergence of those expan…
Formal conjugacy and asymptotic differential algebra
Vincent Bagayoko
We study conjugacy of formal derivations on fields of generalised power series in characteristic 0. Casting the problem of Poincaré resonance in terms of asymptotic differential a…