Groups associated to II 1-factors

Nathanial P. Brown; Valerio Capraro

doi:10.1016/j.jfa.2012.11.003

Groups associated to II ₁-factors

Nathanial P. Brown
, Valerio Capraro

Mathematics

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

We extend recent work of the first named author, constructing a natural Hom semigroup associated to any pair of II ₁-factors. This semigroup always satisfies cancelation, hence embeds into its Grothendieck group. When the target is an ultraproduct of a McDuff factor (e.g., R ^ω), this Grothendieck group turns out to carry a natural vector space structure; in fact, it is a Banach space with natural actions of outer automorphism groups.

Original language	English (US)
Pages (from-to)	493-507
Number of pages	15
Journal	Journal of Functional Analysis
Volume	264
Issue number	2
DOIs	https://doi.org/10.1016/j.jfa.2012.11.003
State	Published - Jan 15 2013

All Science Journal Classification (ASJC) codes

Analysis

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10.1016/j.jfa.2012.11.003

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abstract = "We extend recent work of the first named author, constructing a natural Hom semigroup associated to any pair of II 1-factors. This semigroup always satisfies cancelation, hence embeds into its Grothendieck group. When the target is an ultraproduct of a McDuff factor (e.g., R ω), this Grothendieck group turns out to carry a natural vector space structure; in fact, it is a Banach space with natural actions of outer automorphism groups.",

author = "Brown, \{Nathanial P.\} and Valerio Capraro",

note = "Funding Information: N.B. was supported by NSF-0856197, V.C. by Swiss SNF Sinergia project CRSI22-130435. Corresponding author. E-mail addresses: [email protected] (N.P. Brown), [email protected] (V. Capraro).",

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T1 - Groups associated to II 1-factors

AU - Brown, Nathanial P.

AU - Capraro, Valerio

N1 - Funding Information: N.B. was supported by NSF-0856197, V.C. by Swiss SNF Sinergia project CRSI22-130435. Corresponding author. E-mail addresses: [email protected] (N.P. Brown), [email protected] (V. Capraro).

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N2 - We extend recent work of the first named author, constructing a natural Hom semigroup associated to any pair of II 1-factors. This semigroup always satisfies cancelation, hence embeds into its Grothendieck group. When the target is an ultraproduct of a McDuff factor (e.g., R ω), this Grothendieck group turns out to carry a natural vector space structure; in fact, it is a Banach space with natural actions of outer automorphism groups.

AB - We extend recent work of the first named author, constructing a natural Hom semigroup associated to any pair of II 1-factors. This semigroup always satisfies cancelation, hence embeds into its Grothendieck group. When the target is an ultraproduct of a McDuff factor (e.g., R ω), this Grothendieck group turns out to carry a natural vector space structure; in fact, it is a Banach space with natural actions of outer automorphism groups.

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UR - https://www.scopus.com/pages/publications/84870295368#tab=citedBy

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DO - 10.1016/j.jfa.2012.11.003

M3 - Article

AN - SCOPUS:84870295368

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VL - 264

SP - 493

EP - 507

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 2

ER -

Groups associated to II ₁-factors

Abstract

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