Notes on Drinfeld twists of multiplier Hopf algebras
Volume 157 / 2019
Colloquium Mathematicum 157 (2019), 279-293
MSC: Primary 16T05; Secondary 16T99,
DOI: 10.4064/cm7545-8-2018
Published online: 31 May 2019
Abstract
This paper determines how the integral changes under a Drinfeld twist in multiplier Hopf algebras. For a multiplier Hopf algebra $A$ with a Drinfeld twist $J$, we construct a new multiplier Hopf algebra $A^{J}$. If $A$ is quasitriangular, then so is $A^{J}$. Finally, for a counimodular algebraic quantum group $A$, $A^{J}$ is an algebraic quantum group, and as an application we give a formula for integrals of $H^{J}$, where $H$ is an infinite-dimensional counimodular coFrobenius Hopf algebra.
