On Frobenius-Perron dimension

Li, Changzheng; Shifler, Ryan; Yang, Mingzhi; Zhang, Chi

doi:10.1090/proc/16034

On Frobenius-Perron dimension
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by Changzheng Li, Ryan M. Shifler, Mingzhi Yang and Chi Zhang PDF

Proc. Amer. Math. Soc. 150 (2022), 5035-5045 Request permission

Abstract:

We propose a notion of Frobenius-Perron dimension for certain free $\mathbb {Z}$-modules of infinite rank and compute it for the $\mathbb {Z}$-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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