On a problem about tensor products of subfactors

Xu, Feng

doi:10.1016/j.aim.2013.06.026

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Cited by 3 publications

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An angle between intermediate subfactors and its rigidity

Bakshi

Das

Liu

et al. 2018

Trans. Amer. Math. Soc.

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We introduce a new notion of an angle between intermediate subfactors and prove various interesting properties of the angle and relate it to the Jones index. We prove a uniform 60 60 to 90 90 degree bound for the angle between minimal intermediate subfactors of a finite index irreducible subfactor. From this rigidity we can bound the number of minimal (or maximal) intermediate subfactors by the kissing number in geometry. As a consequence, the number of intermediate subfactors of an irreducible subfactor has at most exponential growth with respect to the Jones index. This answers a question of Longo’s published in 2003.

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An angle between intermediate subfactors and its rigidity

Bakshi

Das

Liu

et al. 2018

Trans. Amer. Math. Soc.

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Ore’s theorem on cyclic subfactor planar algebras and beyond

Palcoux

2018

Pacific J. Math.

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Abstract. Ore proved that a finite group is cyclic if and only if its subgroup lattice is distributive. Now, since every subgroup of a cyclic group is normal, we call a subfactor planar algebra cyclic if all its biprojections are normal and form a distributive lattice. The main result generalizes one side of Ore's theorem and shows that a cyclic subfactor is singly generated in the sense that there is a minimal 2-box projection generating the identity biprojection. We conjecture that this result holds without assuming the biprojections to be normal, and we show that it is true for small lattices. We finally exhibit a dual version of another theorem of Ore and a non-trivial upper bound for the minimal number of irreducible components for a faithful complex representation of a finite group.

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