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Groupoid normalizers of tensor products

By J. Fang, R. Smith, S.A. White and A.D. Wiggins

Abstract

We consider an inclusion B [subset of or equal to] M of finite von Neumann algebras satisfying B′∩M [subset of or equal to] B. A partial isometry vset membership, variantM is called a groupoid normalizer if vBv*,v*Bv[subset of or equal to] B. Given two such inclusions B<sub>i</sub> [subset of or equal to] M<sub>i</sub>, i=1,2, we find approximations to the groupoid normalizers of [formula] in [formula], from which we deduce that the von Neumann algebra generated by the groupoid normalizers of the tensor product is equal to the tensor product of the von Neumann algebras generated by the groupoid normalizers. Examples are given to show that this can fail without the hypothesis [formula], i=1,2. We also prove a parallel result where the groupoid normalizers are replaced by the intertwiners, those partial isometries vset membership, variantM satisfying vBv*[subset of or equal to] B and v*v,vv*[set membership, variant] B

Topics: QA
Publisher: Elsevier
Year: 2010
OAI identifier: oai:eprints.gla.ac.uk:25419
Provided by: Enlighten

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Citations

  1. (1986). Entropy and index for subfactors.
  2. (1977). Ergodic equivalence relations, cohomology, and von Neumann algebras. doi
  3. (2008). Finite von Neumann algbras and masas, doi
  4. (1997). Fundamentals of the theory of operator algebras. doi
  5. (1983). Index for subfactors. doi
  6. (2009). Normalizers of irreducible subfactors. doi
  7. (2006). On a class of type II1 factors with Betti numbers invariants. doi
  8. (1990). On approximation properties for operator spaces. doi
  9. (2009). On completely singular von Neumann subalgebras, doi
  10. (1959). On groups of measure preserving transformation. doi
  11. (2006). On the normalizing algebra of a masa in a II1 factor. arXiv:math.OA/0606225,
  12. (2004). Perturbations of subalgebras of type II1 factors. doi
  13. (1988). Real analysis, third edition.
  14. (1954). Sous-anneaux ab eliens maximaux dans les facteurs de type doi
  15. (2006). Strong rigidity of II1 factors arising from malleable actions of w-rigid groups, doi
  16. (2007). Strong singularity of singular masas in II1 factors.
  17. (1979). Subalgebras of a algebra. doi
  18. (2003). Theory of operator algebras. II, volume 125 of Encyclopaedia of Mathematical Sciences. doi

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