Abstract
Using previous results we construct theq-analogues of the left invariant vector fields of the quantum enveloping algebra corresponding to the complex Lie algebras of typeA n−1 ,B n ,C n , andD n . These quantum vector fields are functionals over the complex quantum groupA. In the special caseA 1 it is shown that this Hopf algebra coincides withU q sl(2, ℂ).
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