  Let G be the group of all formal power series starting with x with
coefficients in a field k of zero characteristic (with the composition
product), and let F[G] be its function algebra. C. Brouder and A. Frabetti
introduced a non-commutative, non-cocommutative graded Hopf algebra H, via a
direct process of ``disabelianisation'' of F[G], i.e. taking the like
presentation of the latter as an algebra but dropping the commutativity
constraint. In this paper we apply a general method to provide four
one-parameters deformations of H, which are quantum groups whose semiclassical
limits are Poisson geometrical symmetries such as Poisson groups or Lie
bialgebras, namely two quantum function algebras and two quantum universal
enveloping algebras. In particular the two Poisson groups are extensions of G,
isomorphic as proalgebraic Poisson varieties but not as proalgebraic groups.
  This analysis easily extends to a hudge family of Hopf algebras of similar
nature, thus yielding a method to associate to such "generalized symmetries"
some classical geometrical symmetries (such as Poisson groups and Lie
bialgebras) in a natural way: the present case then stands as a simplest, toy
model for the general situation.
