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Separable algebras in multitensor C$^*$-categories are unitarizable (2312.12019v2)
Published 19 Dec 2023 in math.OA, math.CT, and math.QA
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.