Some endomorphisms of the hyperfinite $II_1$ factor

dc.creatorHuang, Hsiang-Ping
dc.date2006-02-13
dc.date2006-02-18
dc.date.accessioned2026-07-07T07:03:23Z
dc.date.available2026-07-07T07:03:23Z
dc.descriptionFor 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.identifierhttps://arxiv.org/abs/math/0602284
dc.identifierhttp://arxiv.org/abs/math/0602284
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/108954
dc.subjectOperator Algebras
dc.subject46L37, 47B47
dc.titleSome endomorphisms of the hyperfinite $II_1$ factor
dc.typetext

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