Quantum symmetry algebras of spin systems related to Temperley-Lieb R-matrices
Abstract
A reducible representation of the Temperley-Lieb algebra is constructed on the tensor product of n-dimensional spaces. One obtains as a centraliser of this action a quantum algebra (a quasi-triangular Hopf algebra) Uq with a representation ring equivalent to the representation ring of the sl2 Lie algebra. This algebra Uq is the symmetry algebra of the corresponding open spin chain.
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