Quantum algebras with representation ring of $$ \mathfrak{s}\mathfrak{l}_2 $$ type

A reducible representation of the Temperley-Lieb algebra is constructed on a tensor product of n-dimensional spaces. As a centralizer of this action, we obtain a quantum algebra (quasi-triangular Hopf algebra) with the representation ring that is equivalent to the representation ring of the Lie algebra. Bibliography: 23 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 347, 2007, pp. 167–177.