4 papers · 1 filter
On Simply Connected Simple Lie Skew Braces with Nilpotent Multiplicative Group
Marco Damele, Andrea Loi
We prove that a simply connected simple Lie skew brace with nilpotent multiplicative Lie group must be one-dimensional and abelian. Equivalently, if is a simply c…
Solvability and Rigidity for Topological Skew Braces
Marco Damele, Andrea Loi
We study compact and locally compact topological analogues of the Byott--Vendramin solvability problem for finite skew braces, asking whether solvability of the additive group forc…
On simple compact Lie skew braces
Marco Damele, Andrea Loi
We study simplicity of Lie skew braces from both global and infinitesimal perspectives. After reviewing the correspondence between connected Lie skew braces, simply transitive affi…
Structural and rigidity properties of Lie skew braces
Marco Damele, Andrea Loi
We investigate structural and rigidity properties of \emph{Lie skew braces} (LSBs), objects essentially known in the literature as \emph{post--Lie groups}, obtained by endowing a m…