Reflection equation, twist, and equivariant quantization

We prove that the reflection equation (RE) algebraL _R associated with a finite dimensional representation of a quasitriangular Hopf algebraH is twist-equivalent to the corresponding Faddeev-Reshetikhin-Takhtajan (FRT) algebra. We show thatL _R is a module algebra over the twisted tensor square and the double D( ). We define FRT- and RE-type algebras and apply them to the problem of equivariant quantization on Lie groups and matrix spaces. This research is partially supported by the Israel Academy of Sciences grant no. 8007/99-01.