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