  In our previous paper we have discussed Poisson properties of cluster
algebras of geometric type for the case of a nondegenerate matrix of transition
exponents. In this paper we consider the case of a general matrix of transition
exponents. Our leading idea that a relevant geometric object in this case is a
certain closed 2-form compatible with the cluster algebra structure. The main
example is provided by Penner coordinates on the decorated Teichmueller space,
in which case the above form coincides with the classic Weil-Petersson
symplectic form.

Quantum Algebra