Minimal Index and Dimension for 2-C*-Categories with Finite-Dimensional Centers

@article{Giorgetti2018MinimalIA,
  title={Minimal Index and Dimension for 2-C*-Categories with Finite-Dimensional Centers},
  author={L. Giorgetti and R. Longo},
  journal={Communications in Mathematical Physics},
  year={2018},
  pages={1-39}
}
  • L. Giorgetti, R. Longo
  • Published 2018
  • Mathematics, Physics
  • Communications in Mathematical Physics
  • In the first part of this paper, we give a newlook at inclusions of von Neumann algebras with finite-dimensional centers and finite Jones’ index. The minimal conditional expectation is characterized by means of a canonical state on the relative commutant, that we call the spherical state; the minimal index is neither additive nor multiplicative (it is submultiplicative), contrary to the subfactor case. So we introduce amatrix dimension with the good functorial properties: it is always additive… CONTINUE READING
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