  We develop the Baxterization approach to (an extension of) the quantum group
GL_q(2). We introduce two matrices which play the role of spectral parameter
dependent L-matrices and observe that they are naturally related to two
different comultiplications. Using these comultiplication structures, we find
the related fundamental R-operators in terms of powers of coproducts and also
give their equivalent forms in terms of quantum dilogarithms. The corresponding
quantum local Hamiltonians are given in terms of logarithms of positive
operators. An analogous construction is developed for the q-oscillator and Weyl
algebras using that their algebraic and coalgebraic structures can be obtained
as reductions of those for the quantum group. As an application, the lattice
Liouville model, the q-DST model, the Volterra model, a lattice regularization
of the free field, and the relativistic Toda model are considered.
