The classical dynamic symmetry for the $\mathrm{Sp}(1)$-Kepler problems

Sofiane Bouarroudj, Guowu Meng

A Poisson realization of the simple real Lie algebra ${\mathfrak{so}}^{\ast }(4n)$ on the phase space of each $\mathrm{Sp}(1)$-Kepler problem is exhibited. As a consequence one obtains t…