1 citations · 1 across the 12 of their papers we have counts for
13 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…
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…
Hyperseries subfields of surreal numbers
Vincent Bagayoko
We study subfields of surreal numbers, called hyperseries fields, that are suited to be equipped with derivations and composition laws. We show how to define embeddings on hyperser…
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 al…
Equations over valued groups
Vincent Bagayoko
We study groups, exponential groups and ordered groups equipped with valuations. We investigate algebraic and topological features of such valued structures, and apply our findings…
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…
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…
Sign sequences of log-atomic numbers
Vincent Bagayoko
Log-atomic numbers are surreal numbers whose iterated logarithms are monomials, and consequently have a trivial expansion as transseries. Presenting surreal numbers as sign sequenc…
On ordered groups of regular growth rates
Vincent Mamoutou Bagayoko
We introduce an elementary class of linearly ordered groups, called growth order groups, encompassing certain groups under composition of formal series (e.g. transseries) as well a…
Surreal numbers as hyperseries
Vincent Bagayoko, Joris van der Hoeven
Surreal numbers form the ultimate extension of the field of real numbers with infinitely large and small quantities and in particular with all ordinal numbers. Hyperseries can be r…
The hyperserial field of surreal numbers
Vincent Bagayoko, Joris van der Hoeven
For any ordinal , we show how to define a hyperexponential and a hyperlogarithm on the class of positive infinitely large surreal…
Surreal substructures
Vincent Bagayoko, Joris van der Hoeven
Conway's field No of surreal numbers comes both with a natural total order and an additional "simplicity relation" which is also a partial order. Considering No as a doubly ordered…