  In this paper we study the Goldman bracket between geodesic length functions
both on a Riemann surface $\Sigma_{g,s,0}$ of genus $g$ with $s=1,2$ holes and
on a Riemann sphere $\Sigma_{0,1,n}$ with one hole and $n$ orbifold points of
order two. We show that the corresponding Teichm\"uller spaces $\mathcal
T_{g,s,0}$ and $\mathcal T_{0,1,n}$ are realised as real slices of degenerated
symplectic leaves in the Dubrovin--Ugaglia Poisson algebra of upper--triangular
matrices $S$ with 1 on the diagonal.
