commutators associated to a subfactor and the relative commutant

Hsiang-Ping Huang, University of California at Berkeley

Let $N \subseteq M$ be an inclusion of II₁ factors with finite Jones index. Then $M = N' \cap M \oplus [N, M]$ as a vector space. Here [N, M] denotes the vector space spanned by the commutators of the form [a, b] where a in N, b in M.

98-10-08