An explicit isomorphism between quantum and classical sl(n)

TL;DR

This paper explicitly constructs an isomorphism between quantum and classical sl(n), extending known results from n=2 to general n, clarifying the algebraic relationship.

Contribution

It provides the first explicit construction of the isomorphism for all n, not just for the case n=2, advancing understanding of quantum groups.

Findings

Explicit isomorphism constructed for g=sl(n)

Extends previous results from n=2 to general n

Clarifies algebraic relationship between quantum and classical sl(n)

Abstract

Let g be a complex, semisimple Lie algebra. Drinfeld showed that the quantum group associated to g is isomorphic as an algebra to the trivial deformation of the universal enveloping algebra of g. In this paper we construct explicitly such an isomorphism when g = sl(n), previously known only for n=2.