Cartan subalgebras and bimodule decompositions of II_1 factors - Popa, Sorin; Shlyakhtenko, Dimitri (Mathematica Scandinavica, 2003)
Let AM be a MASA in a II_1 factor M. We describe the von Neumann subalgebra of M generated by A and its normalizer N(A) as the set N_q^w(A) consisting of those elements mM for which the bimodule AmA is discrete. We prove that two MASAs A and B are conjugate by a unitary uN^w_q(A) iff A is discrete over B and B is discrete over A in the sense defined by Feldman and Moore [5]. As a consequence, we show that A is a Cartan subalgebra of M iff for any MASA BM, B=uAu^* for some uM exactly when A is discrete over B and B is discrete over A.