It is well known that the universal enveloping algebra of a semisimple Lie algebra admits no non-trivial deformations as an algebra. In particular, by a cohomological argument, there exists a (non-explicit) isomorphism between the enveloping algebra and the corresponding quantum group. An explicit description of such isomorphism was known only for sl(2).

In this talk, we describe an explicit isomorphism between classical and quantum sl(n) for any n, which relies on an apparently new realisation of the evaluation homomorphism of the Yangian of sl(n). This is a joint work with S. Gautam.