Some endomorphisms of the hyperfinite $II_1$ factor
| dc.creator | Huang, Hsiang-Ping | |
| dc.date | 2006-02-13 | |
| dc.date | 2006-02-18 | |
| dc.date.accessioned | 2026-07-07T07:03:23Z | |
| dc.date.available | 2026-07-07T07:03:23Z | |
| dc.description | For any finite dimensional C*-algebra A with any trace vector {\vec s} whose components are rational numbers, we give an endomorphism Φ of the hyperfinite II_1 factor R such that: forall k in {\mathbb N} Φ^k (R)' \cap R= \otimes^k A The canonical trace τ 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^λ \subset M^λ with trivial relative commutant (N^λ)' \cap M^λ= {\mathbb C} and with the Jones index [M^λ: N^λ]= λ^{-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 λ^{-1} > 4 can occur. | |
| dc.identifier | https://arxiv.org/abs/math/0602284 | |
| dc.identifier | http://arxiv.org/abs/math/0602284 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/108954 | |
| dc.subject | Operator Algebras | |
| dc.subject | 46L37, 47B47 | |
| dc.title | Some endomorphisms of the hyperfinite $II_1$ factor | |
| dc.type | text |