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arXiv · 1110.5543

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

Tao Yang·Xuan Zhou·Juzhen Chen
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Abstract

Based on a pairing of two regular multiplier Hopf algebras $A$ and $B$, Heisenberg double $\mathscr{H}$ is the smash product $A \# B$ with respect to the left regular action of $B$ on $A$. Let $\mathscr{D}=A\bowtie B$ be the Drinfel'd double, then Heisenberg double $\mathscr{H}$ is a Yetter-Drinfel'd $\mathscr{D}$-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.

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Tao Yang, Xuan Zhou, Juzhen Chen. 2011-10-25. Heisenberg double as braided commutative Yetter-Drinfel'd module algebra over Drinfel'd double in multiplier Hopf algebra case. https://doi.org/10.1007/s12188-016-0125-6

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