On the Drinfeld Twist for Quantum sl(2)

TL;DR

This paper explores a twist that relates the quantum deformation of sl(2) to its classical form, providing an explicit universal twisting element up to second order in the deformation parameter.

Contribution

It presents an explicit isomorphism, up to a twist, between the quantum and classical sl(2) algebras and constructs the universal twisting element to second order.

Findings

Explicit universal twisting element up to second order in h

Isomorphism between quantum and classical sl(2) algebras up to a twist

Provides a detailed construction of the twist element

Abstract

An isomorphism, up to a twist, between the quasitriangular quantum enveloping algebra U_h(sl(2)) and the (classical) U(sl(2))[[h]]is discussed. The universal twisting element $\cal F$ is given up to the second order in the deformation parameter $h$.