1-supertransitive subfactors with index at most 6+1/5
Date
2014
Authors
Liu, Zhengwei
Morrison, Scott
Penneys, David
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Volume Title
Publisher
Springer Verlag
Abstract
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 up to a sign'.
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Keywords
Operator Algebras (math.OA), Quantum Algebra (math.QA)
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Source
Communications in Mathematical Physics
Type
Journal article
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Embargo: 2015-06-01