Irreducible subfactors derived from Popa's construction for non-tracial states

Details Irreducible subfactors derived from Popa's construction for non-tracial states Irreducible subfactors derived from Popa's construction for non-tracial states

2000-11-13

arxiv.org/abs/math/0011084v2

Mathematics

Operator Algebras

LaTeX2e amsart class; 17 pages (now single spaced); picture and minor corrections added

Scientific paper

For an inclusion of the form $\Bbb C\subseteq M_n(\Bbb C)$, where $M_n(\Bbb C)$ is endowed with a state with diagonal weights $\lambda=(\lambda_1, ..., \lambda_n)$, we use Popa's construction, for non-tracial states, to obtain an irreducible inclusion of $II_1$ factors, $N^\lambda(Q)\subseteq M^\lambda(Q) $ of index $\sum \frac{1}{\lambda_i}$. $M^\lambda(Q)$ is identified with a subfactor inside the centralizer algebra of the canonical free product state on $Q\star M_N(\Bbb C)$. Its structure is described by ``infinite'' semicircular elements as in \cite{Ra3}. The irreducible subfactor inclusions obtained by this method are similar to the first irreducible subfactor inclusions, of index in $[4,\infty)$ constructed in \cite {Po1}, starting with the Jones' subfactors inclusion $R^s\subseteq R$, $s>4$. In the present paper, since the inclusion we start with has a simpler structure, it is easier to control the algebra structure of the subfactor inclusions.

Affiliated with

Also associated with

No associations

Rating

Irreducible subfactors derived from Popa's construction for non-tracial states 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 Irreducible subfactors derived from Popa's construction for non-tracial states, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Irreducible subfactors derived from Popa's construction for non-tracial states will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-351210