Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4591499 | Journal of Functional Analysis | 2011 | 25 Pages |
Abstract
The notion of sofic equivalence relation was introduced by Gabor Elek and Gabor Lippner. Their technics employ some graph theory. Here we define this notion in a more operator algebraic context, starting from Connesʼ Embedding Problem, and prove the equivalence of these two definitions. We introduce a notion of sofic action for an arbitrary group and prove that an amalgamated product of sofic actions over amenable groups is again sofic. We also prove that an amalgamated product of sofic groups over an amenable subgroup is again sofic.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory