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  1. ; (, Selecta Mathematica)
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  2. ; ; (, Annales Henri Poincaré)
    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 Bischoff et al. (J Funct Anal 281(1):109004, 2021), 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 𝛼-induction and 𝜎-restriction for braided subfactors previously known in the finite index case. 
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  3. ; ; (, Journal of Functional Analysis)
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  4. (, International Journal of Mathematics)
    Using a result of Longo and Xu, we show that the anomaly arising from a cyclic permutation orbifold of order 3 of a holomorphic conformal net [Formula: see text] with central charge [Formula: see text] depends on the “gravitational anomaly” [Formula: see text]. In particular, the conjecture that holomorphic permutation orbifolds are non-anomalous and therefore a stronger conjecture of Müger about braided crossed [Formula: see text]-categories arising from permutation orbifolds of completely rational conformal nets are wrong. More generally, we show that cyclic permutations of order [Formula: see text] are non-anomalous if and only if [Formula: see text] or [Formula: see text]. We also show that all cyclic permutation gaugings of [Formula: see text] arise from conformal nets. 
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  5. ; (, Transformation Groups)
    We prove that commutative algebras in braided tensor categories do not admit faithful Hopf algebra actions unless they come from group actions. We also show that a group action allows us to see the algebra as the regular algebra in the representation category of the acting group. 
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  6. (, Contemporary Mathematics. Topological Phases of Matter and Quantum Computation)
    We give a short proof for a well-known formula for the rank of a G-crossed braided extension of a modular tensor category. 
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    Accepted Manuscript Full Text Available
  7. ; ; ; (, Journal of High Energy Physics)
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