Inhomogeneous Multiparameter Jordanian Quantum Groups by Contraction

It is well–known [1] that, analogous to the classical group–theoretical method, the q–deformation of IGL(2) can be constructed by factoring out a certain two–sided Hopf ideal from the multiparameter q–deformation of GL(3). This is an interesting procedure, allowing, for example, the construction of a differential calculus on the quantum plane by a reduction of the differential calculus on the quantum group. In this paper, we apply the same construction to the Jordanian deformation. The multiparameter Jordanian deformation of GL(3) is first produced by a contraction from the corresponding q–deformation and this is then used to construct the inhomogeneous group by factorisation. The Hopf -structure of IGLJ(2) is given explicitly and we show that it is possible to derive from this a coaction of a modified version of GLJ(2) on the Jordanian quantum plane.