Tangent Lie groups are Riemannian naturally reductive spaces

Ilka Agricola, Ana Cristina Ferreira

Given a compact Lie group $G$ with Lie algebra $\mathfrak{g}$, we consider its tangent Lie group $TG\cong G{⋉}_{\mathrm{Ad}}\mathfrak{g}$. In this short note, we prove that $T…