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 Semikhatov (Commun Algebra 39, 1883–1906, 2011) to some infinite dimensional cases.
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The authors would like to thank the referee for his/her valuable comments. The work was partially sponsored by Qing Lan Project of Jangsu Province and supported by the NNSF of China (No. 11226070, No. 11571173), the NJAUF (No. LXY201201019, No. LXYQ201201103) and NSF for Colleges and Universities in Jiangsu Province (No. 11KJB110004).
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Communicated by Christoph Schweigert.
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Yang, T., Zhou, X. & Chen, J. Heisenberg double as braided commutative Yetter–Drinfel’d module algebra over Drinfel’d double in multiplier Hopf algebra case. Abh. Math. Semin. Univ. Hambg. 87, 23–38 (2017). https://doi.org/10.1007/s12188-016-0125-6
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DOI: https://doi.org/10.1007/s12188-016-0125-6