Quantum symmetry algebras of spin systems related to Temperley-Lieb R-matrices

Details Quantum symmetry algebras of spin systems related to Temperley-Lieb R-matrices Quantum symmetry algebras of spin systems related to Temperley-Lieb R-matrices

2007-12-19

arxiv.org/abs/0712.3154v2

Journal of Mathematical Physics 49 023510 (2008)

Mathematics

Quantum Algebra

14 pages LaTex; typos corrected and two references added

Scientific paper

10.1063/1.2873025

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) U_q with a representation ring equivalent to the representation ring of the sl_2 Lie algebra. This algebra U_q is the symmetry algebra of the corresponding open spin chain.

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