A Hopf Algebra Structure on Uq(sl(2))
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We assume in this chapter that the field k is the field of complex numbers and that q is not a root of unity. We now equip the algebra Uq = Uq (sl(2)) defined in Chapter VI with a Hopf algebra structure. Then we prove that any finite-dimensional Uq-module is a direct sum of the simple modules de-scribed in VI.3. We show later that Uq acts naturally on the quantum plane of IV. 1 and that it is in duality with the Hopf algebra SLq(2) of Chapter IV. We shall also build scalar products on the simple finite-dimensional Uq -modules. We describe the quantum Clebsch-Gordan formula and give the main properties of the quantum Clebsch-Gordan coefficients.
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