Examples
- If we take the algebra A to be the complex numbers C, then the crossed product is called the von Neumann group algebra of G.
- If G is an infinite discrete group such that every conjugacy class has infinite order then the von Neumann group algebra is a factor of type II1. Moreover if every finite set of elements of G generates a finite subgroup (or more generally if G is amenable) then the factor is the hyperfinite factor of type II1.
Read more about this topic: Crossed Product
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