Commutators Associated to a Subfactor and Its Relative Commutants
نویسنده
چکیده
A central problem in subfactor theory is the classification of inclusions of II1 factors, N ⊆M . An important invariant for such an inclusion is the lattice of higher relative commutants, {M ′ i ∩Mj}i,j , known as the standard invariant, contained in the Jones tower N ⊆ M ⊆ M1 · · ·. There are several approaches to studying the standard invariant, namely paragroups [3], λ-lattices [8], and planar algebras [6]. In the geometric framework of planar algebras, the existence of rotation operators is apparent. This is in contrast to the paragroup or λ-lattice setting where the existence of rotation operators is by no means obvious. However, for the moment, the planar algebra framework is restricted to the case then N ⊆M is extremal,
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