Minimal faces and Schur's Lemma for embeddings into R^U

2016/08/29 by Scott Atkinson, Atkinson, Scott
Mathematics · #46A55 #46Lxx #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA) #math.FA #math.OA #msc:46A55 #msc:46Lxx

paper · pdf · doi:10.48550/arxiv.1608.08189

9 pages. Comments welcome!

arxiv created 2016/08/29 · arxiv updated 2016/08/30

Abstract

In the context of N. Brown's Hom(N,R^U), we establish that given π: N → R^U, the dimension of the minimal face containing [π] is one less than the dimension of the center of the relative commutant of π. We also show the "convex independence" of extreme points in the sense that the convex hull of n extreme points is an n-vertex simplex. Along the way, we establish a version of Schur's Lemma for embeddings of II₁-factors.

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