  To a tree of semi-simple algebras we associate a qurve (or formally smooth
algebra) S. We introduce a Zariski- and etale quiver describing the finite
dimensional representations of S. In particular, we show that all quotient
varieties of the etale quiver have a natural Poisson structure induced by a
double Poisson algebra structure on a certain universal localization of its
path algebra. Explicit calculations are included for the group algebras of the
arithmetic groups (P)SL2(Z) and GL2(Z) but the methods apply as well to
congruence subgroups.
