# The hypergroupoid of boundary conditions for local quantum observables

@article{Bischoff2016TheHO,
title={The hypergroupoid of boundary conditions for local quantum observables},
author={M. Bischoff and K. Rehren},
journal={arXiv: Mathematical Physics},
year={2016}
}
• Published 2016
• Physics, Mathematics
• arXiv: Mathematical Physics
• We review the definition of hypergroups by Sunder, and we associate a hypergroup to a type III subfactor $N\subset M$ of finite index, whose canonical endomorphism $\gamma\in\mathrm{End}(M)$ is multiplicity-free. It is realized by positive maps of $M$ that have $N$ as fixed points. If the depth is $>2$, this hypergroup is different from the hypergroup associated with the fusion algebra of $M$-$M$ bimodules that was Sunder's original motivation to introduce hypergroups. We explain how the… CONTINUE READING