# Yangians and quantum loop algebras

@article{Gautam2013YangiansAQ, title={Yangians and quantum loop algebras}, author={Sachin Gautam and Valerio Toledano Laredo}, journal={Selecta Mathematica}, year={2013}, volume={19}, pages={271-336} }

Let $$\mathfrak{g }$$ be a complex, semisimple Lie algebra. Drinfeld showed that the quantum loop algebra $$U_\hbar (L\mathfrak g )$$ of $$\mathfrak{g }$$ degenerates to the Yangian $${Y_\hbar (\mathfrak g )}$$. We strengthen this result by constructing an explicit algebra homomorphism $$\Phi $$ from $$U_\hbar (L\mathfrak g )$$ to the completion of $${Y_\hbar (\mathfrak g )}$$ with respect to its grading. We show moreover that $$\Phi $$ becomes an isomorphism when $${U_\hbar (L\mathfrak g…

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