Coloured Extensions of Quantum Groups

The notion of quantum groups has, in recent years, been generalised by parametrizing the corresponding generators with some continuously varying `colour' variables and the associated algebra and the coalgebra are defined in a way that all Hopf algebraic properties remain preserved. This results in the coloured extension of a quantum group. Focussing on the most intuitive example of GL_q(2), I will establish a picture of duality and construct the corresponding differential calculus. The quantum plane covariant under the action of coloured GL_q(2) will also be exhibited.