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Communications in Mathematical Physics

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

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

  • Zhengwei Liu
  • Scott Morrison
  • David Penneys
Article

Abstract

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.

Keywords

Fusion Category Algebraic Integer Reidemeister Move Minimal Projection Principal Graph 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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