DUALITY FOR THE JORDANIAN MATRIX QUANTUM GROUP GL(G,H)(2)

We find the Hopf algebra U-g,U-h dual to the Jordanian matrix quantum group GL(g,h)(2). As an algebra it depends only on the sum of the two parameters and is split into two subalgebras:U-g,U-h' (with three gene rators) and U(Z) (with one generator). The subalgebra U(Z) is a centra l Hopf subalgebra of U-g,U-h. The subalgebra U-g,U-h' is not a Hopf su balgebra and its co-algebra structure depends on both parameters. We d iscuss also two one-parameter special cases: g = h and g = -h. The sub algebra U-h,U-h' is a Hopf algebra and coincides with the algebra intr oduced by Ohn as the dual of SLh(2). The subalgebra U--h,U-h' is isomo rphic to U(s/(2)) as an algebra but has a nontrivial co-algebra struct ure and again Is not a Hopf subalgebra of U--h,U-h.