EMIS ELibM Electronic Journals Journal of Lie Theory
Vol. 13, No. 1, pp. 21--64 (2003)

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PBW and duality theorems for quantum groups and quantum current algebras

Benjamin Enriquez

B. Enriquez
IRMA and Université Louis Pasteur,
7 rue René Descartes,
67084 Strasbourg, France
enriquez@math.u-strasbg.fr

Abstract: 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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Electronic fulltext finalized on: 22 Nov 2002. This page was last modified: 3 Jan 2003.

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