Journal of Lie Theory 13 (2003), No. 1, 021--064
Copyright Heldermann Verlag 2003
PBW and Duality Theorems for Quantum Groups and Quantum Current Algebras
IRMA, Université Louis Pasteur, 7 rue René Descartes, 67084 Strasbourg, France
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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