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Let SU_q(2) and E_q(2) be Woronowicz' q-deformations of respectively thecompact 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, theirduals are `Morita equivalent locally compact quantum groups'. In more concreteterms, we prove that the von Neumann algebraic quantum groups of `boundedmeasurable functions' on SU_q(2) and E_q(2) are unitary cocycle deformations ofeach other.

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