PBW and duality theorems for quantum groups and quantum current algebras

Details PBW and duality theorems for quantum groups and quantum current algebras PBW and duality theorems for quantum groups and quantum current algebras

1999-04-21

arxiv.org/abs/math/9904113v4

Mathematics

Quantum Algebra

44 pages, mistake in one proof corrected

Scientific paper

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 $A_1^{(1)}$ case.

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