Yangians and quantum loop algebras

Understand

Let g be a complex, semisimple Lie algebra.

• Drinfeld showed that the quantum loop algebra U_h(Lg) of g degenerates to the Yangian Y_h(g).
• We strengthen this result by constructing an explicit algebra homomorphism Phi defined over Q[[h]] from U_h(Lg) to the completion of Y_h(g) with respect to its grading.
• We show moreover that Phi becomes an isomorphism when the quantum loop algebra is completed with respect to its its evaluation ideal.