An algebraic framework for the Drinfeld double based on infinite groupoids

Abstract

In this paper we mainly consider the notion of Drinfeld double for two weak multiplier Hopf (⁎-)algebras which are paired with each other. Then we show that the Drinfeld double is again a weak multiplier Hopf (⁎-)algebra. Furthermore, we study integrals on the Drinfeld double. Finally, we establish the correspondence between modules over a Drinfeld double D(A) and Yetter-Drinfeld modules over a weak algebraic quantum group A.