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On the biparametric quantum deformation of $GL(2) \otimes GL(1)$
We study the biparametric quantum deformation of $GL(2) \otimes GL(1)$ and exhibit its cross-product structure. We derive explicitly the associated dual algebra, i.e., the quantised universal enveloping algebra employing the R-matrix procedure. This facilitates construction of a bicovariant differential calculus which is also shown to have a cross-product structure. Finally, a Jordanian analogue of the deformation is presented as a cross-product algebra.