Galois Correspondence and Fourier Analysis on Local Discrete Subfactors
Galois Correspondence and Fourier Analysis on Local Discrete Subfactors
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DOI：
10.1007/s00023-022-01154-4
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发表时间：
2021-07
期刊：
影响因子：
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通讯作者：
M. Bischoff;Simone Del Vecchio;L. Giorgetti
中科院分区：
文献类型：
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作者：
M. Bischoff;Simone Del Vecchio;L. Giorgetti
离散子因子包括一类特殊的无限指数子因子和所有有限指数子因子。一个离散的子因子被称为局部的，当它是编织的，它满足一个交换性条件的动机，包括量子场论的代数哈格-卡斯特勒设置的研究。在Bischoff等人（J Funct Anal 281（1）：109004，2021）中，我们证明了每个不可约的局部离散子因子在典型紧超群的作用下作为不动点子因子出现。本文证明了中间冯诺依曼代数与闭子超群之间的伽罗瓦对应关系，并在此基础上研究了子因子理论傅里叶变换。沿着的方式，我们延长的主要结果有关的诱导和限制以前已知的编织子因子在有限指数的情况下。
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-induction and-restriction for braided subfactors previously known in the finite index case.