Separable algebras in multitensor C$^*$-categories are unitarizable
Operator Algebras
2024-03-28 v2 Category Theory
Quantum Algebra
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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Cite
@article{arxiv.2312.12019,
title = {Separable algebras in multitensor C$^*$-categories are unitarizable},
author = {Luca Giorgetti and Wei Yuan and XuRui Zhao},
journal= {arXiv preprint arXiv:2312.12019},
year = {2024}
}
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14 pages