Quantum algebras with representation ring of $\operatorname{sl}(2)$ type

A reducible representation of the Temperley–Lieb algebra is constructed on tensor product of $n$-dimensional spaces. One obtains as a centraliser of this action a quantum algebra (a quasitriangular Hopf algebra) with representation ring equivalent to the representation ring of the $\operatorname{sl}(2)$ Lie algebra.