Groups associated to II1-factors
Copyright policy )Groups associated to II1-factors
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., $R^��$), 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.
- Pennsylvania State University United States
- University of Milano-Bicocca Italy
- University of Neuchâtel Switzerland
Mathematics - Operator Algebras, II1-factors, Ultrapowers, II ; 1; -factors; Space of morphisms; Ultrapowers;, Functional Analysis (math.FA), Space of morphisms, Mathematics - Functional Analysis, FOS: Mathematics, Operator Algebras (math.OA), Analysis, II 1-factors; Space of morphisms; Ultrapowers;
Mathematics - Operator Algebras, II1-factors, Ultrapowers, II ; 1; -factors; Space of morphisms; Ultrapowers;, Functional Analysis (math.FA), Space of morphisms, Mathematics - Functional Analysis, FOS: Mathematics, Operator Algebras (math.OA), Analysis, II 1-factors; Space of morphisms; Ultrapowers;
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