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Mathematics > Operator Algebras

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

Authors: Luca Giorgetti, Wei Yuan, XuRui Zhao
(Submitted on 19 Dec 2023 (v1), last revised 27 Mar 2024 (this version, v2))
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.
Comments: 14 pages
Subjects: Operator Algebras (math.OA); Category Theory (math.CT); Quantum Algebra (math.QA)
MSC classes: 46L89 (Primary) 18M20, 46L08 (Secondary)
Journal reference: AIMS Mathematics 9 (2024) 11320-11334. Special Issue Operator Theory: Advances and Applications
DOI: 10.3934/math.2024555
Cite as: arXiv:2312.12019 [math.OA]
  (or arXiv:2312.12019v2 [math.OA] for this version)

Submission history

From: Luca Giorgetti [view email]
[v1] Tue, 19 Dec 2023 10:13:18 GMT (17kb)
[v2] Wed, 27 Mar 2024 11:15:14 GMT (19kb)
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