Abstract
We introduce continuous analogues of Nakayama algebras. In particular, we introduce the notion of (pre-)Kupisch functions, which play a role as Kupisch series of Nakayama algebras, and view a continuous Nakayama representation as a special type of representation of \({\mathbb {R}}\) or \({\mathbb {S}}^1\). We investigate equivalences and connectedness of the categories of Nakayama representations. Specifically, we prove that orientation-preserving homeomorphisms on \({\mathbb {R}}\) and on \({\mathbb {S}}^1\) induce equivalences between these categories. Connectedness is characterized by a special type of points called separation points determined by (pre-)Kupisch functions. We also construct an exact embedding from the category of finite-dimensional representations for any finite-dimensional Nakayama algebra, to a category of continuous Nakayama representaitons.
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Acknowledgements
JR would like to thank Karin M. Jacobsen, Charles Paquette, and Emine Yıldırım for helpful dicussions. SZ would like to thank Shrey Sanadhya for helpful discussions.
Funding
JR is supported at Ghent University by BOF grant 01P12621. SZ is supported by the NSF of China (No. 12201321).
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All authors contributed equally to the study conception and design. Material preparation and analysis was performed by Job Daisie Rock. The first draft of the manuscript was written by Shijie Zhu. All authors read and approved the final manuscript.
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Communicated by Henning Krause.
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Rock, J.D., Zhu, S. Continuous Nakayama Representations. Appl Categor Struct 31, 44 (2023). https://doi.org/10.1007/s10485-023-09748-7
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DOI: https://doi.org/10.1007/s10485-023-09748-7