Communications in Mathematical Physics

, Volume 334, Issue 2, pp 889–922 | Cite as

1-Supertransitive Subfactors with Index at Most \({6\frac{1}{5}}\)



An irreducible II1-subfactor \({A\subset B}\) is exactly 1-supertransitive if \({B\ominus A}\) is reducible as an AA bimodule. We classify exactly 1-supertransitive subfactors with index at most \({6\frac{1}{5}}\), leaving aside the composite subfactors at index exactly 6 where there are severe difficulties. Previously, such subfactors were only known up to index \({3+\sqrt{5} \approx 5.23}\). Our work is a significant extension, and also shows that index 6 is not an insurmountable barrier.

There are exactly three such subfactors with index in \({(3+\sqrt{5}, 6 \frac{1}{5}]}\), all with index \({3+2\sqrt{2}}\). One of these comes from SO(3)q at a root of unity, while the other two appear to be closely related, and are ‘braided up to a sign’.

This is the published version of arXiv:1310.8566.


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Copyright information

© The Author(s) 2014

Authors and Affiliations

  1. 1.Vanderbilt UniversityNashvilleUSA
  2. 2.Mathematical Sciences InstituteAustralian National UniversityCanberraAustralia
  3. 3.University of CaliforniaLos AngelesUSA

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