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On representing some lattices as lattices of intermediate subfactors of finite index

Feng Xu
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Abstract

We prove that the very simple lattices which consist of a largest, a smallest and $2n$ pairwise incomparable elements where $n$ is a positive integer can be realized as the lattices of intermediate subfactors of finite index and finite depth. Using the same techniques, we give a necessary and sufficient condition for subfactors coming from Loop groups of type $A$ at generic levels to be maximal.

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Feng Xu. 2009-05-08. On representing some lattices as lattices of intermediate subfactors of finite index. https://arxiv.org/abs/math/0703248

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