Coloured extension of GL_q(2) and its dual algebra

Deepak Parashar

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Submission date: 27. Feb. 2001
published in: Physics of atomic nuclei, 64 (2001) 12, p. 2146-2150 
DOI number (of the published article): 10.1134/1.1432916
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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.