English

An angle between intermediate subfactors and its rigidity

Operator Algebras 2017-10-03 v1 Functional Analysis

Abstract

We introduce a new notion of angle between intermediate subfactors and prove various interesting properties of the angle and relate it with the Jones' index. We prove a uniform 60 to 90 degree bound for the angle between minimal intermediate subfactors of a finite index irreducible subfactor. From this rigidity we can bound the number of minimal (or maximal) intermediate subfactors by the kissing number in geometry. As a consequence, the number intermediate subfactors of an irreducible subfactor has at most exponential growth with respect to the Jones index. This answers a question of Longo published in 2003.

Keywords

Cite

@article{arxiv.1710.00285,
  title  = {An angle between intermediate subfactors and its rigidity},
  author = {Keshab Chandra Bakshi and Sayan Das and Zhengwei Liu and Yunxiang Ren},
  journal= {arXiv preprint arXiv:1710.00285},
  year   = {2017}
}

Comments

21 pages

R2 v1 2026-06-22T21:59:57.185Z