The Drinfel'd double versus the Heisenberg double for an algebraic quantum group. (Q1878447)

Let \(A\) be a regular multiplier Hopf algebra with nonzero integrals, and let \(\widehat A\) be the dual of \(A\). It is known that \(\langle\widehat A,A\rangle\) is a pairing of multiplier Hopf algebras. The authors prove that the associated Drinfeld double \(D=\widehat A\times A^{\text{cop}}\) is a quasitriangular multiplier Hopf algebra. The product of the dual multiplier Hopf algebra \(\widehat D\) is deformed via a certain right action of \(D\) on \(\widehat D\), relating it to the Heisenberg double \(A\#\widehat A\).