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On Frobenius-Perron dimension

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.

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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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Zhang, Chi0000-0002-1324-2311
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.
Funding AgencyGrant Number
National Natural Science Foundation of China11822113
National Natural Science Foundation of China11831017
National Natural Science Foundation of China11771455
Issue or Number:12
Record Number:CaltechAUTHORS:20221003-756400000.23
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:117213
Deposited By: Melissa Ray
Deposited On:12 Oct 2022 14:01
Last Modified:12 Oct 2022 14:01

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