Galois correspondence and Fourier analysis on local discrete subfactors. (English) Zbl 1502.46050
Summary: 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 [J. Funct. Anal. 281, No. 1, Article ID 109004, 78 p. (2021; Zbl 1481.46066)], 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.
MSC:
| 46L37 | Subfactors and their classification |
| 81T99 | Quantum field theory; related classical field theories |
| 43A62 | Harmonic analysis on hypergroups |
Citations:
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