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

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

2009-12-22

arxiv.org/abs/0912.4350v2

Mathematics

Quantum Algebra

28 pages; added some references, corrected some typos, and provided an extra remark at the end of the third section

Scientific paper

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.

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