Coloured extension of GL_q(2) and its dual algebra

Abstract

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

10 pages LaTeX. Talk given at the "XXIII International Colloquium on Group Theoretical Methods in Physics", July 31 - August 05, 2000, Dubna (Russia); to appear in the proceedings