A (2n+1)-dimensional quantum group constructed from a skew-symmetric matrix

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.