Hamiltonian structures of the integrable field theory models

It is shown that for classical continuous integrable models of the field theory the Poisson bracket given in the r-matrix form allows a simple geometrical interpretation in current algebra terms. The model phase spaces for the given interpretation are integral varieties of standard simplex structure in current algebra. Integral varieties of discrete r-matrix bracket for rational r-matrices related with the classical Lie algebras are built explicitly. It is shown that in the discrete case there is a multiplicative averaging operation permitting to determine trigonometrical and elliptical L-operators from the rational ones. For the one-pole L-operator related with Sl(2) algebra such averaging is calculated explicitly