Heisenberg double as braided commutative Yetter-Drinfel'd module algebra over Drinfel'd double in multiplier Hopf algebra case

Abstract

Based on a pairing of two regular multiplier Hopf algebras $A$ and $B$, Heisenberg double $\mathcal{H}$ is the smash product $A\#B$ with respect to the left regular action of $B$ on $A$. Let $\mathcal{D}=A\bowtie B$ be the Drinfel'd double, then Heisenberg double $\mathcal{H}$ is a Yetter-Drinfel'd $\mathcal{D}$-module algebra, and it is also braided commutative by the braiding of Yetter-Drinfel'd module, which generalizes the results in [10] to some infinite dimensional cases.

18 pages. arXiv admin note: text overlap with arXiv:math/0404029 by other authors

References in corpus (1)

• Heisenberg double H(B^*) as a braided commutative Yetter-Drinfeld module algebra over the Drinfeld double