The ergodic commutant conjecture for sofic groups
The ergodic commutant conjecture for sofic groups
Let be a sofic group, let be the universal sofic group, and let be the Loeb measure space. For an embedding , write for the subgroup of elements in commuting with .
Ergodic commutant conjecture. Every sofic group admits an embedding such that the action
is ergodic.
A positive answer would remove the subamenability assumption in the theorem discussed immediately before this conjecture and would provide a route to constructing non-sofic groups via amalgamated products without amenable amalgams. The supplied text does not state that the conjecture has been resolved.
Sources & referencesView supporting material
Primary source
Ben Hayes and Srivatsav Kunnawalkam Elayavalli, “On sofic approximations of non amenable groups”, arXiv:2306.04713 (2024).
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