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arXiv · 2107.09345

Galois Correspondence and Fourier Analysis on Local Discrete Subfactors

Marcel Bischoff·Simone Del Vecchio·Luca Giorgetti
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Abstract

Discrete subfactors include a particular class of infinite index subfactors and all finite index ones. A discrete subfactor is called local when it is braided and it fulfills a commutativity condition motivated by the study of inclusion of Quantum Field Theories in the algebraic Haag-Kastler setting. In [BDG21], we proved that every irreducible local discrete subfactor arises as the fixed point subfactor under the action of a canonical compact hypergroup. In this work, we prove a Galois correspondence between intermediate von Neumann algebras and closed subhypergroups, and we study the subfactor theoretical Fourier transform in this context. Along the way, we extend the main results concerning $\alpha$-induction and $\sigma$-restriction for braided subfactors previously known in the finite index case.

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BibTeXRIS

Marcel Bischoff, Simone Del Vecchio, Luca Giorgetti. 2021-07-20. Galois Correspondence and Fourier Analysis on Local Discrete Subfactors. https://doi.org/10.1007/s00023-022-01154-4

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