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

Journal Article · Fri Feb 15 00:00:00 EST 2008 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.2873025· OSTI ID:21013837

Kulish, P P ^[1]; Manojlovic, N; Nagy, Z ^[2]

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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)

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.

• OSTI ID: 21013837
• Journal Information: Journal of Mathematical Physics, Vol. 49, Issue 2; Other Information: DOI: 10.1063/1.2873025; (c) 2008 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALGEBRA
QUANTUM MECHANICS
R MATRIX
SL GROUPS
SPIN
SYMMETRY
TENSORS