On quantization of r-matrices for Belavin-Drinfeld Triples

Abstract

We suggest a formula for quantum universal $R$-matrices corresponding to quasitriangular classical $r$-matrices classified by Belavin and Drinfeld for all simple Lie algebras. The $R$-matrices are obtained by twisting the standard universal $R$-matrix.

12 pages, LaTeX

References in corpus (3)

• Quantum Dilogarithm
• Twisting of quantum (super)algebras. Connection of Drinfeld's and Cartan-Weyl realizations for quantum affine algebras
• Heisenberg Double and Pentagon Relation

Cited by in corpus (7)

• On Some Lie Bialgebra Structures on Polynomial Algebras and their Quantization
• Twisted Quantum Deformations of Lorentz and Poincaré algebras
• Braids, Shuffles and Symmetrizers
• Once again about quantum deformations of D=4 Lorentz algebra: twistings of q-deformation
• Semi-classical twists for sl(3) and sl(4) boundary r-matrices of Cremmer-Gervais type
• Basic quantizations of $D=4$ Euclidean, Lorentz, Kleinian and quaternionic ${\mathfrak{o}}^{\star }(4)$ symmetries
• Drinfeld-Jimbo quantum Lie algebra