Universal R-matrices for non-standard (1+1) quantum groups

Universal R–matrices for non-standard (1+1) quantum groups

A universal quasitriangular R–matrix for the non-standard quantum (1+1) Poincaré algebra Uziso(1, 1) is deduced by imposing analyticity in the deformation parameter z. A family gμ of “quantum graded contractions” of the algebra Uziso(1, 1)⊕U−ziso(1, 1) is obtained; this set of quantum algebras contains as Hopf subalgebras with two primitive translations quantum analogues of the two dimensional ...

Universal R-matrix for Non-standard Quantum Sl(2, Ir)

A universal R-matrix for the non-standard (Jordanian) quantum deformation of sl(2, IR) is presented. A family of solutions of the quantum Yang– Baxter equation is obtained from some finite dimensional representations of this Lie bialgebra quantization of sl(2, IR). The quantum Yang–Baxter equation (YBE) R12R13R23 = R23R13R12. (1) was discovered to play a relevant role as the integrability condi...

Quantum groupoids associated to universal dynamical R-matrices

By using twist construction, we obtain a quantum groupoid D⊗qUqg for any simple Lie algebra g. The underlying Hopf algebroid structure encodes all the information of the corresponding elliptic quantum group-the quasi-Hopf algebras as obtained by Fronsdal, Arnaudon et. al. and Jimbo et. al.. Groupöıdes quantiques associés à des R-matrices dynamiques universelles Résumé En utlisant une constructi...

Non-standard Quantum Groups and Superization

We obtain the universal R-matrix of the non-standard quantum group associated to the Alexander-Conway knot polynomial. We show further that this nonstandard quantum group is related to the super-quantum group Uqgl(1|1) by a general process of superization, which we describe. We also study a twisted variant of this non-standard quantum group and obtain, as a result, a twisted version of Uqgl(1|1...

CLASSICAL r - MATRICES AND CONSTRUCTION OF QUANTUM GROUPS