Quantum and super-quantum group related to the Alexander-Conway polynomial

Abstract

We describe the quasitriangular structure (universal $R$-matrix) on the non-standard quantum group $U_q(H_1,H_2,X^{\pm })$ associated to the Alexander-Conway matrix solution of the Yang-Baxter equation. We show that this Hopf algebra is connected with the super-Hopf algebra $U_{q}gl(1|1)$ by a general process of superization.

arXiv comment8 pages, LaTex file, Talk given at the XXVIII Karpacz Winter School, Karpacz, Poland, February 1992