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.
Brown, P., Capraro, V. (2013). Groups associated to II 1-factors. JOURNAL OF FUNCTIONAL ANALYSIS, 264(2), 493-507 [10.1016/j.jfa.2012.11.003].
Groups associated to II 1-factors
Capraro, V
2013
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.
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