Sofic groups and direct finiteness
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 groups.
math.RA↗
arXiv subjects
Publications and source records attributed to G. Elek.
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 groups.
Answering some queries of Weiss, we prove that the free product and amenable extensions of sofic groups are sofic as well, and give an example of a finitely generated sofic group that is not residually amenable.