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Quantum Symmetries of the Twisted Tensor Products of C*-Algebras

  • Jyotishman Bhowmick
  • Arnab Mandal
  • Sutanu Roy
  • Adam Skalski
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Abstract

We consider the construction of twisted tensor products in the category of C*-algebras equipped with orthogonal filtrations and under certain assumptions on the form of the twist compute the corresponding quantum symmetry group, which turns out to be the generalized Drinfeld double of the quantum symmetry groups of the original filtrations. We show how these results apply to a wide class of crossed products of C*-algebras by actions of discrete groups. We also discuss an example where the hypothesis of our main theorem is not satisfied and the quantum symmetry group is not a generalized Drinfeld double.

Notes

Acknowledgments

The second author was supported by the National Postdoctoral Fellowship given by SERB-DST, Government of India Grant No. PDF/2017/001795. The third author was partially supported by an Early Career Research Award given by SERB-DST, Government of India Grant No. ECR/2017/001354. The last author was partially supported by the National Science Centre (NCN) Grant No. 2014/14/E/ST1/00525. This work was started during the internship of the second author at IMPAN in 2016, funded by the Warsaw Center for Mathematical Sciences. A.M. thanks A.S. for his kind hospitality at IMPAN. We thank the referees for their thoughtful comments and suggestions.

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© The Author(s) 2018

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  • Jyotishman Bhowmick
    • 1
  • Arnab Mandal
    • 2
  • Sutanu Roy
    • 2
  • Adam Skalski
    • 3
  1. 1.Statistics and Mathematics UnitIndian Statistical InstituteKolkataIndia
  2. 2.School of Mathematical SciencesNational Institute of Science Education and Research Bhubaneswar, HBNIJatniIndia
  3. 3.Institute of Mathematics of the Polish Academy of SciencesWarsawPoland

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