Corpus ID: 119733575

Structure of bicentralizer algebras and inclusions of type III factors

  title={Structure of bicentralizer algebras and inclusions of type III factors},
  author={Hiroshi Ando and Uffe Haagerup and Cyril Houdayer and Amine Marrakchi},
  journal={arXiv: Operator Algebras},
We investigate the structure of the relative bicentralizer algebra ${\rm B}(N \subset M, \varphi)$ for inclusions of von Neumann algebras with normal expectation where $N$ is a type ${\rm III_1}$ subfactor and $\varphi \in N_*$ is a faithful state. We first construct a canonical flow $\beta^\varphi : \mathbf R^*_+ \curvearrowright {\rm B}(N \subset M, \varphi)$ on the relative bicentralizer algebra and we show that the W$^*$-dynamical system $({\rm B}(N \subset M, \varphi), \beta^\varphi)$ is… Expand
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