Drinfel'd twist of multiplier Hopf algebras

Abstract

This paper generalizes the Drinfel'd twist to the multiplier Hopf algebra case. For a multiplier Hopf algebra $A$ with a twist $J$, we construct a new multiplier Hopf algebra $A^{J}$. Furthermore, if $A$ is quasitriangular, then $A^{J}$ is also. Finally, for a counimodular algebraic quantum group $A$, $A^{J}$ is an algebraic quantum group.