A Closed Expression for the Universal R-Matrix in a Non-Standard Quantum Double

Abstract

In recent papers of the author, a method was developed for constructing quasitriangular Hopf algebras (quantum groups) of the quantum-double type. As a by-product, a novel non-standard example of the quantum double has been found. In the present paper, a closed expression (in terms of elementary functions) for the corresponding universal R-matrix is obtained. In reduced form, when the number of generators becomes two instead of four, this quantum group can be interpreted as a deformation of the Lie algebra [x,h]=2h in the context of Drinfeld's quantization program.

6 pages, LATEX, JINR preprint E2-93-159

Cited by in corpus (24)

• Extended jordanian twists for Lie algebras
• $h$-Deformation as a Contraction of $q$-Deformation
• Chains of twists for classical Lie algebras
• Deformed Yangians and Integrable Models
• Universal $R$-matrix for non-standard quantum $sl(2,\mathbb{R})$
• Multiparametric quantum gl(2): Lie bialgebras, quantum R-matrices and non-relativistic limits
• Duality for the Jordanian Matrix Quantum Group $G{L}_{g,h}(2)$
• Twist Deformation of the rank one Lie Superalgebra
• Peripheric Extended Twists
• Universal $R$--matrices for non-standard (1+1) quantum groups
• Twist maps for non-standard quantum algebras and discrete Schrodinger symmetries
• Quantization of Drinfel'd doubles
• Extended and Reshetikhin Twists for sl(3)
• The Drinfeld double gl(n) \oplus t_n
• The Twisted Heisenberg Algebra ${\mathcal{U}}_{h,w}(\mathcal{H}(4))$
• Duality for Exotic Bialgebras
• Super-Jordanian Quantum Superalgebra ${\mathcal{U}}_h(osp(2/1))$
• Quantizations of D=3 Lorentz symmetry
• The Jordanian deformation of su(2) and Clebsch-Gordan coefficients
• Universal R-matrix for null-plane quantized Poincar{é} algebra
• New time-type and space-type non-standard quantum algebras and discrete symmetries
• Universal R operator with Jordanian deformation of conformal symmetry
• Nonstandard Poincare and Heisenberg Algebras
• Maps between Deformed and Ordinary Gauge Fields