# MathSciDoc: An Archive for Mathematician ∫

#### Quantum AlgebraSpectral Theory and Operator Algebramathscidoc:2206.29001

Communications in Mathematical Physics, 334, 889–922, 2014.9
An irreducible II_1-subfactor A⊂B is exactly 1-supertransitive if B⊖A is reducible as an A − A bimodule. We classify exactly 1-supertransitive subfactors with index at most 6+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} ≈ 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+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’.
@inproceedings{zhengwei20141-supertransitive,
title={1-Supertransitive Subfactors with Index at Most 6+1/5},
author={Zhengwei Liu, Scott Morrison, and David Penneys},
url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220626170911162062471},
booktitle={Communications in Mathematical Physics},
volume={334},
pages={889–922},
year={2014},
}

Zhengwei Liu, Scott Morrison, and David Penneys. 1-Supertransitive Subfactors with Index at Most 6+1/5. 2014. Vol. 334. In Communications in Mathematical Physics. pp.889–922. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220626170911162062471.