Algebraic construction of quantum integrable models including inhomogeneous models

Exploiting the quantum integrability condition we construct an ancestor mod el associated with a new underlying quadratic algebra. This ancestor model represents an exactly integrable quantum lattice inhomogeneous anisotropic model and at its various realizations and limits can generate a wide range of integrable models. They cover quantum lattice as well as field models as sociated with the quantum R-matrix of trigonometric type or at the undeform ed q --> 1 limit similar models belonging to the rational class. The classi cal limit likewise yields the corresponding classical discrete and field mo dels. Thus along with the generation of known integrable models in a unifyi ng way a new class of inhomogeneous models including variable mass sine-Gor don model, inhomogeneous Toda chain, impure spin chains, etc., are construc ted.