1IRMA, Université Louis Pasteur, 7 rue René Descartes, 67084 Strasbourg, France 2We 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 3case. 4[
Journal of Lie Theory, Tome 13 (2003) no. 1, pp. 21-64
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Benjamin 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/JOLT_2003_13_1_a3/
@article{JOLT_2003_13_1_a3,
author = {Benjamin Enriquez},
title = {PBW and {Duality} {Theorems} for {Quantum} {Groups} and {Quantum} {Current} {Algebras}},
journal = {Journal of Lie Theory},
pages = {21--64},
year = {2003},
volume = {13},
number = {1},
url = {http://geodesic.mathdoc.fr/item/JOLT_2003_13_1_a3/}
}
TY - JOUR
AU - Benjamin Enriquez
TI - PBW and Duality Theorems for Quantum Groups and Quantum Current Algebras
JO - Journal of Lie Theory
PY - 2003
SP - 21
EP - 64
VL - 13
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UR - http://geodesic.mathdoc.fr/item/JOLT_2003_13_1_a3/
ID - JOLT_2003_13_1_a3
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%T PBW and Duality Theorems for Quantum Groups and Quantum Current Algebras
%J Journal of Lie Theory
%D 2003
%P 21-64
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%U http://geodesic.mathdoc.fr/item/JOLT_2003_13_1_a3/
%F JOLT_2003_13_1_a3
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.
