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Title: 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 centralizer of this action a quantum algebra (a quasitriangular Hopf algebra) U{sub q} with a representation ring equivalent to the representation ring of the sl{sub 2} Lie algebra. This algebra U{sub q} is the symmetry algebra of the corresponding open spin chain.

Authors:
 [1]; ;  [2]
  1. St. Petersburg Department of Steklov Mathematical Institute, Fontanka 27, 191023 St. Petersburg (Russian Federation)
  2. Departamento de Matematica, F. C. T., Universidade do Algarve, Campus de Gambelas, PT-8005-139 Faro (Portugal)
Publication Date:
OSTI Identifier:
21013837
Resource Type:
Journal Article
Journal Name:
Journal of Mathematical Physics
Additional Journal Information:
Journal Volume: 49; Journal Issue: 2; Other Information: DOI: 10.1063/1.2873025; (c) 2008 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0022-2488
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGEBRA; QUANTUM MECHANICS; R MATRIX; SL GROUPS; SPIN; SYMMETRY; TENSORS

Citation Formats

Kulish, P P, Manojlovic, N, Nagy, Z, and Grupo de Fisica Matematica, Universidade de Lisboa. Quantum symmetry algebras of spin systems related to Temperley-Lieb R-matrices. United States: N. p., 2008. Web. doi:10.1063/1.2873025.
Kulish, P P, Manojlovic, N, Nagy, Z, & Grupo de Fisica Matematica, Universidade de Lisboa. Quantum symmetry algebras of spin systems related to Temperley-Lieb R-matrices. United States. https://doi.org/10.1063/1.2873025
Kulish, P P, Manojlovic, N, Nagy, Z, and Grupo de Fisica Matematica, Universidade de Lisboa. 2008. "Quantum symmetry algebras of spin systems related to Temperley-Lieb R-matrices". United States. https://doi.org/10.1063/1.2873025.
@article{osti_21013837,
title = {Quantum symmetry algebras of spin systems related to Temperley-Lieb R-matrices},
author = {Kulish, P P and Manojlovic, N and Nagy, Z and Grupo de Fisica Matematica, Universidade de Lisboa},
abstractNote = {A reducible representation of the Temperley-Lieb algebra is constructed on the tensor product of n-dimensional spaces. One obtains as a centralizer of this action a quantum algebra (a quasitriangular Hopf algebra) U{sub q} with a representation ring equivalent to the representation ring of the sl{sub 2} Lie algebra. This algebra U{sub q} is the symmetry algebra of the corresponding open spin chain.},
doi = {10.1063/1.2873025},
url = {https://www.osti.gov/biblio/21013837}, journal = {Journal of Mathematical Physics},
issn = {0022-2488},
number = 2,
volume = 49,
place = {United States},
year = {Fri Feb 15 00:00:00 EST 2008},
month = {Fri Feb 15 00:00:00 EST 2008}
}