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

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

1996-02-07

arxiv.org/abs/q-alg/9602020v1

Mathematics

Quantum Algebra

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

Scientific paper

10.1007/BF02909182

The dually conjugate Hopf algebras $Fun_{p,q}(R)$ 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 ${\cal T}$-matrix for $Fun_{p,q}(R)$ is derived. While expressing an arbitrary group element of the quantum group characterized by the noncommuting parameters in a representation independent way, the ${\cal T}$-matrix generalizes the familiar exponential relation between a Lie group and its Lie algebra. The universal ${\cal R}$-matrix and the FRT matrix generators, $L^{(\pm )}$, for $U_{p,q}(R)$ are derived from the ${\cal T}$-matrix.

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