The dual (p, q)-Alexander-Conway Hopf algebras and the associated universal ℐ-matrix (original) (raw)

1996, Zeitschrift für Physik C: Particles and Fields

The dually conjugate Hopf algebras F un 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 Tmatrix for F un 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 T -matrix generalizes the familiar exponential relation between a Lie group and its Lie algebra. The universal R-matrix and the FRT matrix generators, L (±) , for U p,q (R) are derived from the T -matrix.

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