  To the Yang-Baxter equation an additional relation can be added. This is the
reflection equation which appears in various places, with or without spectral
parameter. For example, in factorizable scattering on a half-line, integrable
lattice models with non-periodic boundary conditions, non-commutative
differential geometry on quantum groups, etc. We study two forms of spectral
parameter independent reflection equations, 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 we give the constant solutions of the reflection
equations. Various quadratic algebras defined by the reflection equations are
also given explicitly.
