Groups associated to II₁-factors

Brown, Nathanial P.; Capraro, Valerio

doi:10.1016/j.jfa.2012.11.003

arXiv 2012-05-13 DOI 10.1016/j.jfa.2012.11.003 0 views

Groups associated to II₁-factors

Brown, Nathanial P. · Capraro, Valerio

Operator Algebras Functional Analysis

Original · EN

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.

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