LAX EQUATIONS AND QUANTUM GROUPS

We construct Lax equations associated to quantum groups. In particular we derive quantum trace formulas for the Lax matrix L giving the quantum analogue of its usual classical invariants generated by tr(Ln). These quantities generate an abelian subalgebra of the quantum group and define hamiltonian flows that admit quantum Lax representations. This hierarchy of quantum Lax equations is shown to verify zero-curvature relations. In the field theory case we give the lattice construction of these quantum structures. © 1990.