  Using recent results on string on $AdS_{3}\times N^d$, where N is a
d-dimensional compact manifold, we re-examine the derivation of the non trivial
extension of the (1+2) dimensional-Poincar\'e algebra obtained by Rausch de
Traubenberg and Slupinsky, refs [1] and [29]. We show by explicit computation
that this new extension is a special kind of fractional supersymmetric algebra
which may be derived from the deformation of the conformal structure living on
the boundary of $AdS_3$. The two so(1,2) Lorentz modules of spin $\pm{1\over
k}$ used in building of the generalisation of the (1+2) Poincar\'e algebra are
re-interpreted in our analysis as highest weight representations of the left
and right Virasoro symmetries on the boundary of $AdS_3$. We also complete
known results on 2d-fractional supersymmetry by using spectral flow of affine
Kac-Moody and superconformal symmetries. Finally we make preliminary comments
on the trick of introducing Fth-roots of g-modules to generalise the so(1,2)
result to higher rank lie algebras g.
