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It it known that to get the usual Hamiltonian formulation of latticeYang-Mills theory in the temporal gauge $A_{0}=0$ one should place on everylink the cotangent bundle of a Lie group. The cotangent bundle may beconsidered as a limiting case of a so called Heisenberg double of a Lie groupwhich is one of the basic objects in the theory of Lie-Poisson and quantumgroups. It is shown in the paper that there is a generalization of the usualHamiltonian formulation to the case of the Heisenberg double.Comment: 11 pages, latex, no figure

GAUGE-INVARIANT HAMILTONIAN FORMULATION OF LATTICE YANG-MILLS THEORY AND THE HEISENBERG DOUBLE