On a Morita equivalence between the duals of quantum SU(2) and quantum E(2)

Let SU_q(2) and E_q(2) be Woronowicz’ q-deformations of respectively the compact Lie group SU(2) and the non-trivial double cover of the Lie group E(2) of Euclidian transformations of the plane. We prove that, in some sense, their duals are Morita equivalent locally compact quantum groups'. In more concrete terms, we prove that the von Neumann algebraic quantum groups of bounded measurable functions’ on SU_q(2) and E_q(2) are unitary cocycle deformations of each other.