Twisted tensor coproduct of multiplier Hopf algebras

Abstract

We put a non-trivial comultiplication on the natural tensor product algebra of two multiplier Hopf algebras by means of a "cotwisting map." As a special case we characterize the dual of the Drinfel'd double of an algebraic quantum group. Because any finite-dimensional Hopf algebra is an algebraic quantum group, our characterization applies to the dual of the Drinfel'd double of a finite-dimensional Hopf algebra. Then it coincides with a result of Lu. (C) 2004 Elsevier Inc. All rights reserved.