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Mathematics > Operator Algebras

arXiv:2210.00792 (math)
[Submitted on 3 Oct 2022]

Title:Complete Positivity of Comultiplication and Primary Criteria for Unitary Categorification

Authors:Linzhe Huang, Zhengwei Liu, Sebastien Palcoux, Jinsong Wu
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Abstract:In this paper, we investigate quantum Fourier analysis on subfactors and unitary fusion categories. We prove the complete positivity of the comultiplication for subfactors and derive a primary $n$-criterion of unitary categorifcation of multifusion rings. It is stronger than the Schur product criterion when $n\geq3$. The primary criterion could be transformed into various criteria which are easier to check in practice even for noncommutative, high-rank, high-multiplicity, multifusion rings. More importantly, the primary criterion could be localized on a sparse set, so that it works for multifusion rings with sparse known data. We give numerous examples to illustrate the efficiency and the power of these criteria.
Comments: 34 pages
Subjects: Operator Algebras (math.OA); Mathematical Physics (math-ph); Category Theory (math.CT); Quantum Algebra (math.QA)
MSC classes: 46L37, 43A32, 18M20, 57R56
Cite as: arXiv:2210.00792 [math.OA]
  (or arXiv:2210.00792v1 [math.OA] for this version)
  https://doi.org/10.48550/arXiv.2210.00792

Submission history

From: Zhengwei Liu [view email]
[v1] Mon, 3 Oct 2022 09:59:21 UTC (30 KB)
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