tools of differential analysis, like for instance in [@OldRedBook]: primarily the notion of tangent map and the exponential map $\exp:{\mathfrak{g}}\to G$. For the benefit of the readers, Lie group and Lie algebra actions are reviewed in Appendix A. The basics of Hopf algebra are a prerequisite. Unless otherwise specified, we consider Hopf algebras over the complex numbers. We briefly introduce our notations for them, which are like in [@Quaoar]; the pedagogical paper [@FresasSalvajes] is recommended as well. Given an associative algebra with unit $H\ni1_H=:u(1_{\mathbb{C}})$, then $H{\otimes}H$ is associative with bilinear multiplication given by $(a{\otimes}b)(c{\otimes}d)=ac{\otimes}bd$ on decomposable tensors, and unit $1_H{\otimes}1_H$. Write just 1 for the unit element of $H$ henceforth. One says $H$ is a bialgebra if algebra morphisms $\eta:H\to{\mathbb{C}}$ (augmentation) and ${\Delta}:H\to H{\otimes}H$ (coproduct) are defined, such that the maps $(\eta{\otimes}{{\mathrm{id}}}){\Delta}$ and $({{\mathrm{id}}}{\otimes}\eta){\Delta}$ from $H$ to $H$ coincide with the identity map ${{\mathrm{id}}}$ and $({\Delta}{\otimes}{{\mathrm{id}}}){\Delta}$ and $({{\mathrm{id}}}{\otimes}{\Delta}){\Delta}$ from $H$ to $H{\otimes}H{\otimes}H$ also coincide (we omit the sign $\circ$ for composition of linear maps). One says $H$ is a Hopf algebra if it furthermore possesses an antiautomorphism $S$, the *antipode*, such that $m(S{\otimes}{{\mathrm{id}}}){\Delta}=m(S{\otimes}{{\mathrm{id}}}){\Delta}=u\eta$; where $m:H{\otimes}H\to H$ denotes the algebra map. Familiarity with enveloping algebras and the Poincaré–Birkhoff–Witt and Cartier–Milnor–Moore theorems 