  In earlier work (*) we studied an extension of the canonical symplectic
structure in the cotangent bundle of an affine space ${\cal Q}={\bf R}^N$, by
additional terms implying the Poisson non-commutativity of both configuration
and momentum variables. In this article, we claim that such an extension can be
done consistently when ${\cal Q}$ is a Lie group $G$. -- (*) : F.J.Vanhecke,
C.Sigaud and A.R.da Silva, arXiv:math-phys/0502003 and Braz.J.Phys.{\bf 36},no
IB,194(2006)
