Li, Changzheng and Shifler, Ryan M. and Yang, Mingzhi and Zhang, Chi (2022) On Frobenius-Perron dimension. Proceedings of the American Mathematical Society, 150 (12). pp. 5035-5045. ISSN 0002-9939. doi:10.1090/proc/16034. https://resolver.caltech.edu/CaltechAUTHORS:20221003-756400000.23
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Abstract
We propose a notion of Frobenius-Perron dimension for certain free ℤ-modules of infinite rank and compute it for the ℤ-modules of finite dimensional complex representations of unitary groups with nonnegative dominant weights. The definition of Frobenius-Perron dimension that we are introducing naturally generalizes the well-known Frobenius-Perron dimension on the category of finite dimensional complex representations of a finite group.
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| Additional Information: | The first author was supported by NSFC Grants 11822113, 11831017 and 11771455. The authors would like to thank Hongjia Chen, Leonardo C. Mihalcea, Kyoji Saito, Peng Shan, Wei Yuan and Ming Zhang for helpful discussions. The authors would also like to thank an anonymous referee for bringing our attention to references on the literature on the theory of rigid C∗-tensor categories. | ||||||||
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| Issue or Number: | 12 | ||||||||
| DOI: | 10.1090/proc/16034 | ||||||||
| Record Number: | CaltechAUTHORS:20221003-756400000.23 | ||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20221003-756400000.23 | ||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||||
| ID Code: | 117213 | ||||||||
| Collection: | CaltechAUTHORS | ||||||||
| Deposited By: | Melissa Ray | ||||||||
| Deposited On: | 12 Oct 2022 14:01 | ||||||||
| Last Modified: | 12 Oct 2022 14:01 |
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