Forked Temperley-Lieb Algebras and Intermediate Subfactors

Details Forked Temperley-Lieb Algebras and Intermediate Subfactors Forked Temperley-Lieb Algebras and Intermediate Subfactors

2006-07-14

arxiv.org/abs/math/0607335v4

Mathematics

Operator Algebras

19 pages. Stylistic revisions and reference added to Evans-Gould 1994 in which forked TL algebras appear

Scientific paper

We consider noncommuting pairs P,Q of intermediate subfactors of an irreducible, finite-index inclusion N in M of II_1 factors such that P and Q are supertransitive with Jones index less than 4 over N. We show that up to isomorphism of the standard invariant, there is a unique such pair corresponding to each even value [P:N]=4cos^2(pi/2n) but none for the odd values [P:N]=4cos^2 (pi/(2n+1)). We also classify the angle values which occur between pairs of intermediate subfactors with small index over their intersection: if [P:N] < 4, then the unique nontrivial angle value is always cos^-1 (1/([P:N]-1)).

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