Drinfel'd twist of multiplier Hopf algebras

TL;DR

This paper extends the concept of Drinfel'd twist to multiplier Hopf algebras, showing how to construct new twisted algebras that preserve quasitriangularity and quantum group properties.

Contribution

It introduces a generalized Drinfel'd twist for multiplier Hopf algebras and demonstrates the preservation of key structures like quasitriangularity and algebraic quantum group status.

Findings

Construction of $A^{J}$ from $A$ with a twist $J$

Preservation of quasitriangularity in $A^{J}$

$A^{J}$ remains an algebraic quantum group if $A$ is counimodular

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.