1-supertransitive subfactors with index at most \(6\frac{1}{5}\). (English) Zbl 1330.46062
Summary: An irreducible \(\mathrm{II}_1\)-subfactor \(A\subset B\) is exactly 1-supertransitive if \(B\ominus A\) is reducible as an \(A\)-\(A\) 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 \(\mathrm{SO}(3)_q\) 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.
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 \(\mathrm{SO}(3)_q\) 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.
MSC:
| 46L37 | Subfactors and their classification |
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