Groups associated to $I{I}_1$-factors

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., $R^{\omega }$), 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.

References in corpus (1)

• On the axiomatization of convex subsets of Banach spaces

Cited by in corpus (3)

• Dedekind complete posets from sheaves on von Neumann algebras
• Minimal faces and Schur's Lemma for embeddings into R^U
• On Krein-Milman theorem for the space of sofic representations