Bicrossproduct Structure of Affine Quantum Groups

Abstract

We show that the affine quantum group $U_q(\widehat{s{l}_2})$ is isomorphic to a bicrossproduct central extension $C Z{}_χ\cross U_q(Lsl_2)$ of the quantum loop group $U_q(Ls{l}_2)$ by a quantum cocycle $\chi$, which we construct. We prove the same result for $U_q(\hat{g})$ in R-matrix form.

arXiv commentLATEX 10 pages