Abstract
Beginning with a skew-symmetric matrix, we define a certain Poisson–Lie group. Its Poisson bracket can be viewed as a cocycle perturbation of the linear (or “Lie–Poisson”) Poisson bracket. By analyzing this Poisson structure, we gather enough information to construct a C ∗ -algebraic locally compact quantum group, via the “cocycle bicrossed product construction” method. The quantum group thus obtained is shown to be a deformation quantization of the Poisson–Lie group, in the sense of Rieffel.
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