Abstract
The paper is devoted to locally compact quantum groups that are related to the classical ‘ax+b’ group. We discuss in detail the quantization of the deformation parameter assumed with no justification in the previous paper. Next we construct (on the C*-level) a larger family of quantum deformations of the ‘ax+b’ group corresponding to the deformation parameter q2 running over an interval in the unit circle. To this end, beside the reflection operator β known from the previous paper we use a new unitary generator w. It commutes with a, b and βwβ=ssgnbw, where s ∈ S1 is a new deformation parameter related to q2. At the end we discuss the groups at roots of unity.
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Communicated by A. Connes
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Pusz, W., Woronowicz, S. A New Quantum Deformation of ‘ax+b’ Group. Commun. Math. Phys. 259, 325–362 (2005). https://doi.org/10.1007/s00220-005-1395-5
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DOI: https://doi.org/10.1007/s00220-005-1395-5