2 papers
math.DS2024
Uniform Borel Amenability
Gábor Elek, Ádám Timár
We study a uniform, quantitative form of the amenability-hyperfiniteness paradigm for bounded-degree Borel graphs generating countable Borel equivalence relations. We introduce \em…
math.RA2003
Sofic groups and direct finiteness
G. Elek, E. Szabo
We construct an analogue of Neumann's affiliated algebras for sofic group algebras over arbitrary fields. Consequently, we settle Kaplansky's direct finiteness conjecture for sofic…