Groups associated to $II_1$-factors
Operator Algebras
2013-09-18 v3 Functional Analysis
Abstract
We extend recent work of the first named author, constructing a natural Hom semigroup associated to any pair of II-factors. This semigroup always satisfies cancelation, hence embeds into its Grothendieck group. When the target is an ultraproduct of a McDuff factor (e.g., ), 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.
Cite
@article{arxiv.1205.2862,
title = {Groups associated to $II_1$-factors},
author = {Nathanial P. Brown and Valerio Capraro},
journal= {arXiv preprint arXiv:1205.2862},
year = {2013}
}