A non co-hyperlinear IRS exists on any non-abelian free group, yielding via simplified reduction an equivalence relation whose von Neumann algebra is not Connes embeddable.
Hyperlinearity, essentially free actions and $L^2$-invariants. The sofic property
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
We prove that Connes' Embedding Conjecture holds for the von Neumann algebras of sofic groups, that is sofic groups are hyperlinear. Hence we provide some new examples of hyperlinearity. We also show that the Determinant Conjecture holds for sofic groups as well. We introduce the notion of essentially free actions and amenable actions and study their properties.
fields
math.OA 1years
2025 1verdicts
UNVERDICTED 1representative citing papers
citing papers explorer
-
There Is An Equivalence Relation Whose von Neumann Algebra Is Not Connes Embeddable
A non co-hyperlinear IRS exists on any non-abelian free group, yielding via simplified reduction an equivalence relation whose von Neumann algebra is not Connes embeddable.