Groups associated to II 1-factors

Nathanial Brown, Valerio Capraro

Research output: Contribution to journalArticle

3 Citations (Scopus)

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 languageEnglish (US)
Pages (from-to)493-507
Number of pages15
JournalJournal of Functional Analysis
Volume264
Issue number2
DOIs
StatePublished - Jan 15 2013

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Grothendieck Group
Semigroup
Ultraproduct
Outer Automorphism Groups
Cancellation
Vector space
Banach space
Target

All Science Journal Classification (ASJC) codes

  • Analysis

Cite this

Brown, Nathanial ; Capraro, Valerio. / Groups associated to II 1-factors. In: Journal of Functional Analysis. 2013 ; Vol. 264, No. 2. pp. 493-507.
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Groups associated to II 1-factors. / Brown, Nathanial; Capraro, Valerio.

In: Journal of Functional Analysis, Vol. 264, No. 2, 15.01.2013, p. 493-507.

Research output: Contribution to journalArticle

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