  Exploiting the quantum integrability condition we construct an ancestor model
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
associated with the quantum $R$-matrix of trigonometric type or at the
undeformed $q \to 1$ limit similar models belonging to the rational class. The
classical limit likewise yields the corresponding classical discrete and field
models. Thus along with the generation of known integrable models in a unifying
way a new class of inhomogeneous models including variable mass sine-Gordon
model, inhomogeneous Toda chain, impure spin chains etc. are constructed.

High Energy Physics - Theory;Exactly Solvable and Integrable Systems;Exactly Solvable and Integrable Systems