CONSTANT SOLUTIONS OF REFLECTION EQUATIONS AND QUANTUM GROUPS

To the Yang-Baxter equation an additional relation can be added. This is the reflection equation that appears in various places, with or without spectral parameter, e.g., in factorizable scattering on a half-line, integrable lattice models with nonperiodic boundary conditions, noncommutative differential geometry on quantum groups, etc. Two forms of spectral-parameter-independent reflection equations are studied, chosen by the requirement that their solutions be comodules with respect to the quantum group coaction leaving invariant the reflection equations. For a variety of known solutions of the Yang-Baxter equation the constant solutions of the reflection equations are given. Various quadratic algebras defined by the reflection equations are also given explicitly.