Mathematics – Operator Algebras
Scientific paper
2006-02-13
Mathematics
Operator Algebras
Scientific paper
For any finite dimensional C*-algebra A with any trace vector {\vec s} whose components are rational numbers, we give an endomorphism {\Phi} of the hyperfinite II_1 factor R such that: forall k in {\mathbb N} {\Phi}^k (R)' \cap R= \otimes^k A The canonical trace {\tau} on R extends the trace vector {\vec s} on A. As a corollary, we construct a one-parameter family of inclusions of hyperfinite II_1 factors N^{\lambda} \subset M^{\lambda} with trivial relative commutant (N^{\lambda})' \cap M^{\lambda}= {\mathbb C} and with the Jones index [M^{\lambda}: N^{\lambda}]= \lambda^{-1} \in (4, \infty) \cap {\mathbb Q} This partially solves the problem of finding all possible values of indices of subfactors with trivial relative commutant in the hyperfinite II_1 factor, by showing that any rational number \lambda^{-1} > 4 can occur.
No associations
LandOfFree
Some endomorphisms of the hyperfinite $II_1$ factor does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Some endomorphisms of the hyperfinite $II_1$ factor, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Some endomorphisms of the hyperfinite $II_1$ factor will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-568310