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Research Article | Open Access

Separable algebras in multitensor C ∗ -categories are unitarizable

Luca Giorgetti1( ), Wei Yuan2,3, XuRui Zhao3
Dipartimento di Matematica, Università di Roma Tor Vergata, Via della Ricerca Scientifica, 1, I-00133 Roma, Italy
Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China
School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
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Abstract

S. Carpi et al. (Comm. Math. Phys., 402 (2023), 169–212) 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.

Keywords

multitensor C∗-categoryseparable algebraunitarily separable algebraC∗-Frobenius algebraQ-system
CLC number: 18M20, 46L08, 46L89

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AIMS Mathematics
Volume 9 Issue 5,
May 2024
Pages 11320-11334
DOI: 10.3934/math.2024555

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Cite this article:
Giorgetti L, Yuan W, Zhao X. Separable algebras in multitensor C ∗ -categories are unitarizable. AIMS Mathematics, 2024, 9(5): 11320-11334. https://doi.org/10.3934/math.2024555

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Received: 20 December 2023
Revised: 11 March 2024
Accepted: 13 March 2024
Published: 15 May 2024
©2024 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)