  It it known that to get the usual Hamiltonian formulation of lattice
Yang-Mills theory in the temporal gauge $A_{0}=0$ one should place on every
link the cotangent bundle of a Lie group. The cotangent bundle may be
considered as a limiting case of a so called Heisenberg double of a Lie group
which is one of the basic objects in the theory of Lie-Poisson and quantum
groups. It is shown in the paper that there is a generalization of the usual
Hamiltonian formulation to the case of the Heisenberg double.
