Coloured extension of GL_q(2) and its dual algebra

Details Coloured extension of GL_q(2) and its dual algebra Coloured extension of GL_q(2) and its dual algebra

2001-02-20

arxiv.org/abs/math/0102163v1

Phys. Atom. Nucl. 64 (2001) 2146-2150

Mathematics

Quantum Algebra

10 pages LaTeX. Talk given at the "XXIII International Colloquium on Group Theoretical Methods in Physics", July 31 - August 0

Scientific paper

10.1134/1.1432916

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.

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