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

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

2007-03-09

arxiv.org/abs/math/0703248v2

Mathematics

Operator Algebras

39 pages, latex, corrected proof of Cor. 5.23. To appear in Advance in Mathematics

Scientific paper

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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