Abstract
We study glued tensor and free products of compact matrix quantum groups with cyclic groups – so-called tensor and free complexifications. We characterize them by studying their representation categories and algebraic relations. In addition, we generalize the concepts of global colourization and alternating colourings from easy quantum groups to arbitrary compact matrix quantum groups. Those concepts are closely related to tensor and free complexification procedures. Finally, we also study a more general procedure of gluing and ungluing.
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08 February 2021
A Correction to this paper has been published: https://doi.org/10.1007/s10468-020-10021-x
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Acknowledgments
I would like to thank to my PhD supervisor Moritz Weber for numerous comments and suggestions regarding the text. I also thank to Adam Skalski and Pierre Tarrago for inspiring discussions on the topic. The article is a part of the author’s PhD thesis.
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Open Access funding enabled and organized by Projekt DEAL. The author was supported by the collaborative research centre SFB-TRR 195 “Symbolic Tools in Mathematics and their Application”.
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Presented by: Alistair Savage
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The original online version of this article was revised: The equation found in page 21 is incorrect. Also, the author names of reference 17 and 18 found in the Reference list are incorrect. These errors have been corrected herein.
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Gromada, D. Gluing Compact Matrix Quantum Groups. Algebr Represent Theor 25, 53–88 (2022). https://doi.org/10.1007/s10468-020-10010-0
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DOI: https://doi.org/10.1007/s10468-020-10010-0