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2024, Volume 9, Issue 5: 11320-11334. doi: 10.3934/math.2024555
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Separable algebras in multitensor C$ ^* $-categories are unitarizable

  • 1.
    Dipartimento di Matematica, Università di Roma Tor Vergata, Via della Ricerca Scientifica, 1, I-00133 Roma, Italy
  • 2.
    Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China
  • 3.
    School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
  • Received: 20 December 2023 Revised: 11 March 2024 Accepted: 13 March 2024 Published: 22 March 2024

  • MSC : 18M20, 46L08, 46L89

  • 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.

    Citation: Luca Giorgetti, Wei Yuan, XuRui Zhao. Separable algebras in multitensor C$ ^* $-categories are unitarizable[J]. AIMS Mathematics, 2024, 9(5): 11320-11334. doi: 10.3934/math.2024555

    Related Papers:

  • 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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