The dual $(p,q)$-Alexander-Conway Hopf algebras and the associated universal $\mathcal{T}$-matrix

Abstract

The dually conjugate Hopf algebras $Fu{n}_{p,q}(R)$ and $U_{p,q}(R)$ associated with the two-parametric $(p,q)$-Alexander-Conway solution $(R)$ of the Yang-Baxter equation are studied. Using the Hopf duality construction, the full Hopf structure of the quasitriangular enveloping algebra $U_{p,q}(R)$ is extracted. The universal $\mathcal{T}$-matrix for $Fu{n}_{p,q}(R)$ is derived. While expressing an arbitrary group element of the quantum group characterized by the noncommuting parameters in a representation independent way, the $\mathcal{T}$-matrix generalizes the familiar exponential relation between a Lie group and its Lie algebra. The universal $\mathcal{R}$-matrix and the FRT matrix generators, $L^{(\pm )}$, for $U_{p,q}(R)$ are derived from the $\mathcal{T}$-matrix.

LaTeX, 15 pages, to appear in Z. Phys. C: Particles and Fields

References in corpus (5)

• Free-Field Representation of Group Element for Simple Quantum Group
• Finite dimensional representations of the quantum group $G{L}_{p,q}(2)$ using the exponential map from $U_{p,q}(gl(2))$
• Exponential mapping for non semisimple quantum groups
• On a nonstandard two-parametric quantum algebra and its connections with $U_{p,q}(gl(2))$ and $U_{p,q}(gl(1|1))$
• The exponential map for representations of $U_{p,q}(gl(2))$