TY - JOUR
T1 - Groups associated to II 1-factors
AU - Brown, Nathanial P.
AU - Capraro, Valerio
N1 - Funding Information:
N.B. was supported by NSF-0856197, V.C. by Swiss SNF Sinergia project CRSI22-130435. Corresponding author. E-mail addresses: [email protected] (N.P. Brown), [email protected] (V. Capraro).
PY - 2013/1/15
Y1 - 2013/1/15
N2 - 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.
AB - 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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U2 - 10.1016/j.jfa.2012.11.003
DO - 10.1016/j.jfa.2012.11.003
M3 - Article
AN - SCOPUS:84870295368
SN - 0022-1236
VL - 264
SP - 493
EP - 507
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
IS - 2
ER -