AIMS Mathematics (Mar 2024)

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

  • Luca Giorgetti ,
  • Wei Yuan,
  • XuRui Zhao

DOI
https://doi.org/10.3934/math.2024555
Journal volume & issue
Vol. 9, no. 5
pp. 11320 – 11334

Abstract

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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.

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