Crossed Product - Examples

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

Famous quotes containing the word examples:

    “It is hardly to be believed how spiritual reflections when mixed with a little physics can hold people’s attention and give them a livelier idea of God than do the often ill-applied examples of his wrath.”
    —G.C. (Georg Christoph)

    “There are many examples of women that have excelled in learning, and even in war, but this is no reason we should bring ‘em all up to Latin and Greek or else military discipline, instead of needle-work and housewifry.”
    —Bernard Mandeville (1670–1733)

    “Histories are more full of examples of the fidelity of dogs than of friends.”
    —Alexander Pope (1688–1744)