From the Tetrahedron Equation to Universal R-Matrices

Abstract

Modified universal R-matrices, associated with the central extension (through the Drinfeld's double construction) of the quantum groups U_q(sl_n), are realized through an infinite dimensional spectral parameter dependent solution for the tetrahedron equation, provided a certain identity on $q$-exponentials holds true.

11 pages, no figures, latex2e

References in corpus (9)

• Hirota equation as an example of integrable symplectic map
• On Discrete 3-Dimensional Equations Associated with the Local Yang-Baxter Relation
• Functional Tetrahedron Equation
• Cyclic monodromy matrices for sl(n) trigonometric R-matrices
• Free-Field Representation of Group Element for Simple Quantum Group
• Affine Toda field theory as a 3-dimensional integrable system
• Group-like elements in quantum groups, and Feigin's conjecture
• Solutions of the functional tetrahedron equation connected with the local Yang -- Baxter equation for the ferro-electric
• Quantum Dilogarithm and Tetrahedron Equation

Cited by in corpus (8)

• On the Yang-Baxter equation for the six-vertex model
• Non-commutative bi-rational maps satisfying Zamolodchikov equation, and Desargues lattices
• Tetrahedron equation and quantum R matrices for $q$-oscillator representations of $U_q(A_{2n}^{(2)}),U_q(C_n^{(1)})$ and $U_q(D_{n+1}^{(2)})$
• Matrix product solutions to the reflection equation from three dimensional integrability
• On a Class of Representations of Quantum Groups
• Quantum holonomic link invariants derived from stated skein algebras
• Supersymmetry and the Modular Double
• On the continuous series for affine sl(2,R)