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Published December 2022 | public
Journal Article

On Frobenius-Perron dimension

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.

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.

Additional details

Created:
August 22, 2023
Modified:
October 24, 2023