  We study the triple $(G,\pi,\prs)$ where $G$ is a connected and simply
connected Lie group, $\pi$ and $\prs$ are, respectively, a multiplicative
Poisson tensor and a left invariant Riemannian metric on $G$ such that the
necessary conditions, introduced by Hawkins, to the existence of a non
commutative deformation (in the direction of $\pi$) of the spectrale triple
associated to $\prs$ are satisfied. We show that the geometric problem of the
classification of such triple $(G,\pi,\prs)$ is equivalent to an algebraic one.
We solve this algebraic problem in low dimensions and we give the list of all
$(G,\pi,\prs)$ satisfying Hawkins's conditions, up to dimension four.
