Abstract
This paper constructs two representations of the quantum groupU q g' by exploiting its quotient structure and the quantum double construction. Here the quantum group is taken as the dual to the quantised algebraU q g, a one parameter deformation of the universal enveloping algebra of the Lie algebra g, as in Drinfel'd [6] and Jimbo [10]. From the two representations, the Hopf structure of the quantised algebraU q g is reexpressed in a matrix format. This is the very structure given by Faddeev et al. [7], in their approach to defining quantum groups and quantised algebras via the quantisation of the function space of the associated Lie group to g.
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Communicated by J. Fröhlich
Supported by a SERC studentship
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Burroughs, N. Relating the approaches to quantised algebras and quantum groups. Commun.Math. Phys. 133, 91–117 (1990). https://doi.org/10.1007/BF02096556
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DOI: https://doi.org/10.1007/BF02096556