Quantum deformations of the Heisenberg group obtained by geometric quantization (Q1176457)

The authors classify all the multiplicative Poisson structures \(G\) on simply connected Heisenberg groups \(G\). They show that each such structure is linearizable; in fact, the exponential map is a Poisson isomorphism from \({\mathcal G}\) to \(G\). Then they prove that \(G\) as a Poisson manifold is integrable and construct in an explicit way its symplectic groupoid \(\Gamma\). Finally a geometric quantization procedure is applied to \(\Gamma\) yielding a wide class of pre-\(C^*\)-algebras which provide quantum deformations of the Heisenberg groups.