Topological dynamical systems associated to II1-factors
By N. Brown. 2010
48 citations recorded by the source corpus.
Abstract If N ⊂ R ω is a separable II1-factor, the space H om ( N , R ω ) of unitary equivalence classes of unital ⁎-homomorphisms N → R ω is shown to have a surprisingly rich structure. If N is not hyperfinite, H om ( N , R ω ) is an infinite-dimensional, complete, metrizable topological space with convex-like structure, and the outer automorphism group Out ( N ) acts on it by “affine” homeomorphisms. (If N ≅ R , then H om ( N , R ω ) is just a point.) Property (T) is reflected in the extreme points – theyʼre discrete in this case. For certain free products N = Σ ⁎ R , every countable group acts nontrivially on H om ( N , R ω ) , and we show the extreme points are not discrete for these examples. Finally, we prove that the dynamical systems associated to free group factors are isomorphic.
Subfields: Algebra and Number Theory, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/451bf7ae739e1b2f949d7c431761c865f8388a60
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In Algebra and Number Theory
In Mathematical Physics
Citations in the corpus
- Introduction to Sofic and Hyperlinear Groups and Connes' Embedding Conjecture (2013, background): “Brown[9]) We say that (X, d) has a convex-like structure if for each n ∈ N and for each μ ∈ Probn there is a map γμ : X(n) → X such that 1.”