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) 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.

arXiv comment14 pages LaTex; typos corrected and two references added

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Cited by in corpus (12)

• Quantum spin chains of Temperley-Lieb type: periodic boundary conditions, spectral multiplicities and finite temperature
• Temperley-Lieb Algebra, Yang-Baxterization and Universal Gate
• Reflection $K$-matrices related to Temperley-Lieb $R$-matrices
• Symmetries of spin systems and Birman-Wenzl-Murakami algebra
• Universal Bethe ansatz solution for the Temperley-Lieb spin chain
• Algebraic classification of Hietarinta's solutions of Yang-Baxter equations~:~invertible $4\times 4$ operators
• Temperley-Lieb R-matrices from generalized Hadamard matrices
• Murphy elements from the double-row transfer matrix
• The Yang-Baxter integrability of the critical Ising chain
• Method of constructing braid group representation and entanglement in a Yang-Baxter sysytem
• Junction type representations of the Temperley-Lieb algebra and associated symmetries
• Quantum Integrability and Quantum Groups: a special issue in memory of Petr P. Kulish