Abstract
A quadrilateral of factors is an irreducible inclusion of factors N ⊂ M with intermediate subfactors P and Q such that P and Q generate M and the intersection of P and Q is N. We investigate the structure of a noncommuting quadrilateral of factors with all the elementary inclusions P ⊂ M, Q ⊂ M, N ⊂ P, and N ⊂ Q 2-supertransitive. In particular, we classify noncommuting quadrilaterals with the indices of the elementary subfactors less than or equal to 4. We also compute the angles between P and Q for quadrilaterals coming from α-induction and asymptotic inclusions.
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