Cartan subalgebras and bimodule decompositions of II1 factors

Authors

  • Sorin Popa
  • Dimitri Shlyakhtenko

DOI:

https://doi.org/10.7146/math.scand.a-14395

Abstract

Let AM be a MASA in a II1 factor M. We describe the von Neumann subalgebra of M generated by A and its normalizer N(A) as the set Nwq(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 uNwq(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.

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Published

2003-03-01

How to Cite

Popa, S., & Shlyakhtenko, D. (2003). Cartan subalgebras and bimodule decompositions of II1 factors. MATHEMATICA SCANDINAVICA, 92(1), 93–102. https://doi.org/10.7146/math.scand.a-14395

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Section

Articles