Nguyen Viet Hai

Abstract
Using $\star$-product on co-adjoint orbits (K-orbits) of  the MD$_4$-groups  we obtain quantum co-adjoint orbits via Fedosov deformation quantization. From this we obtain the full list of corresponding irreducible unitary representations of  the exponential MD$_4$-groups. For groups G$_{4,2,3(\frac{\pi}{2})}$; G$_{4,2,4}$;  
G$_{4,3,4(\frac{\pi}{2})}$ and G$_{4,4,1}$, which are neither nilpotent nor exponential, we obtain also the explicit formulas.