  A novel algebra underlying integrable systems is shown to generate and unify
a large class of quantum integrable models with given $R$-matrix, through
reductions of an ancestor Lax operator and its different realizations. Along
with known discrete and field models a new class of inhomogeneous and impurity
models are obtained.

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