Geodesic
PBW and Duality Theorems for Quantum Groups and Quantum Current Algebras
Journal of Lie theory, Tome 13 (2003) no. 1, pp. 21-64.

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We give proofs of the PBW and duality theorems for the quantum Kac-Moody algebras and quantum current algebras, relying on Lie bialgebra duality.  We also show that the classical limit of the quantum current algebras associated with an untwisted affine Cartan matrix is the enveloping algebra of a quotient of the corresponding toroidal algebra;  this quotient is trivial in all cases except the A1( 1 ) case. 
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     author = {B. Enriquez },
     title = {PBW and {Duality} {Theorems} for {Quantum} {Groups} and {Quantum} {Current} {Algebras}},
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B. Enriquez . PBW and Duality Theorems for Quantum Groups and Quantum Current Algebras. Journal of Lie theory, Tome 13 (2003) no. 1, pp. 21-64. http://geodesic.mathdoc.fr/item/JLT_2003_13_1_JLT_2003_13_1_a3/