Refine search
Actions for selected content:
1 results
There is an equivalence relation whose von Neumann algebra is not Connes embeddable
- Part of
-
- Journal:
- Compositio Mathematica / Volume 162 / Issue 8 / August 2026
- Published online by Cambridge University Press:
- 30 September 2026, pp. 1851-1868
- Print publication:
- August 2026
-
- Article
-
- You have access
- Open access
- HTML
- Export citation
-
The landmark quantum complexity result MIP
$^*$ 
$=$ RE has been used to prove the existence of a non-Connes-embeddable tracial von Neumann algebra. Recently, similar ideas have been used to give a negative solution to the Aldous–Lyons conjecture: there is a non-co-sofic invariant random subgroup (IRS) on any non-abelian free group. We define a notion of hyperlinearity for an IRS and show that there is a non-co-hyperlinear IRS on any non-abelian free group. As a corollary, we prove that there is a relation whose von Neumann algebra is not Connes embeddable. We do this by significantly simplifying the reduction of Aldous–Lyons to non-local games, removing the need for subgroup tests entirely.
