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.
Keywords
Cite
@article{arxiv.math/0102163,
title = {Coloured extension of GL_q(2) and its dual algebra},
author = {Deepak Parashar},
journal= {arXiv preprint arXiv:math/0102163},
year = {2009}
}
Comments
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