  Inspired by factorized scattering from delta-type impurities in
(1+1)-dimensional space-time, we propose and analyse a generalization of the
Zamolodchikov-Faddeev algebra. Distinguished elements of the new algebra,
called reflection and transmission generators, encode the particle-impurity
interactions. We describe in detail the underlying algebraic structure. The
relative Fock representations are explicitly constructed and a general
factorized scattering theory is developed in this framework.
