Representations of the quantum double of the restricted quantum group ūq(sl₂)

Let q be a primitive $2p$-th root of unity with p≥2, and let H=D(ūq(sl₂)) be the Drinfeld double of the restricted quantum group ūq(sl₂). We describe the dual Hopf algebra and the cross relations of H. A change of generator gives a classification of the simple H-modules. Their isomorphism classes are indexed by Z₂ₚ\,2. We construct their projective covers, compute their dimensions, and determine which simple modules are projective. Finally, we prove that H is strictly wild for every p≥2 by constructing a fully faithful exact functor from finite-dimensional x,y-modules to finite-dimensional H-modules.