English

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

Quantum Algebra 2013-08-13 v2

Abstract

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.

Keywords

Cite

@article{arxiv.0912.4350,
  title  = {On a Morita equivalence between the duals of quantum SU(2) and quantum E(2)},
  author = {K. De Commer},
  journal= {arXiv preprint arXiv:0912.4350},
  year   = {2013}
}

Comments

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