Groups associated to II1-factors

We extend recent work of the first named author, constructing a natural Hom semigroup associated to any pair of II1-factors. This semigroup always satisfies cancelation, hence embeds into its Grothendieck group. When the target is an ultraproduct of a McDuff factor (e.g., Rω), this Grothendieck grou...

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Bibliographic Details
Published in:Journal of functional analysis 2013-01, Vol.264 (2), p.493-507
Main Authors: Brown, Nathanial P., Capraro, Valerio
Format: Article
Language:English
Subjects:
II1-factors
Space of morphisms
Ultrapowers
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Summary:We extend recent work of the first named author, constructing a natural Hom semigroup associated to any pair of II1-factors. This semigroup always satisfies cancelation, hence embeds into its Grothendieck group. When the target is an ultraproduct of a McDuff factor (e.g., Rω), 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.
ISSN:0022-1236
1096-0783
DOI:10.1016/j.jfa.2012.11.003