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arXiv · 2312.12019

Separable algebras in multitensor C$^*$-categories are unitarizable

Luca Giorgetti·Wei Yuan·XuRui Zhao
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Abstract

Recently, S. Carpi et al. (Comm. Math. Phys., 402:169-212, 2023) proved that every connected (i.e. haploid) Frobenius algebra in a tensor C$^*$-category is unitarizable (i.e. isomorphic to a special C$^*$-Frobenius algebra). Building on this result, we extend it to the non-connected case by showing that an algebra in a multitensor C$^*$-category is unitarizable if and only if it is separable.

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Luca Giorgetti, Wei Yuan, XuRui Zhao. 2023-12-19. Separable algebras in multitensor C$^*$-categories are unitarizable. https://doi.org/10.3934/math.2024555

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