Duality for the Gr,s Quantum Group
Abstract
The two parameter quantum group Gr,s is generated by five elements, four of which form a Hopf subalgebra isomorphic to GLq(2), while the fifth generator relates Gr,s to GLp,q(2). We construct explicitly the dual algebra of Gr,s and show that it is isomorphic to the single parameter deformation of gl(2) + gl(1), with the second parameter appearing in the costructure. We also formulate a differential calculus on Gr,s which provides a realisation of the calculus on GLp,q(2).
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