May you formulate and extend the introduction of the above article by adding some words on Poisson-Lie groups and the Big Bracket formalism, with the additional referee review: The problem is an interesting one: Flatness and metaflatness conditions have been shown by Hawkins to be related to deformations issues arising in (formal) deformation quantization of Poisson structures and therefore one should expect that quantizing Poisson-Lie groups which integrates the Lie bialgebras listed here should produce quantum groups with a good behaviours in terms of NC geometry à la Connes. The paper relies on the classification of flat Lie algebras provided by Milnor.