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math.GR2026
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…
math.GR2026
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…
math.GR2025
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…