Colored extension of GLq(2) and its dual algebra

We address the problem of duality between the colored extension of the quantized algebra of functions on a group and that of its quantized universal enveloping algebra, i.e., its dual. In particular, we derive explicitly the algebra dual to the colored extension of GLq(2) using the colored RLL relations and exhibit its Hopf structure. This leads to a colored generalization of the R-matrix procedure to construct a bicovariant differential calculus on the colored version of GLq(2). In addition, we also propose a colored generalization of the geometric approach to quantum group duality given by Sudbery and Dobrev