## 1-supertransitive subfactors with index at most 6+1/5

### Description

We classify irreducible II_1 subfactors A \subset B such that B \ominus A is reducible as an A-A bimodule, with index at most 6+1/5, leaving aside the composite subfactors at index exactly 6. Previous work has already achieved this up to index 3+\sqrt{5} \approx 5.23. We find 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...[Show more]

Collections ANU Research Publications 2014 Journal article http://hdl.handle.net/1885/11574 Communications in Mathematical Physics 10.1007/s00220-014-2160-4