Hyperfinite type II factor
In mathematics, there are up to isomorphism exactly two separably acting hyperfinite type II factors; one infinite and one finite. Murray and von Neumann proved that up to isomorphism there is a unique von Neumann algebra that is a factor of type II1 and also hyperfinite; it is called the hyperfinite type II1 factor. There are an uncountable number of other factors of type II1. Connes proved that the infinite one is also unique.
The hyperfinite II1 factor R is the unique smallest infinite dimensional factor in the following sense: it is contained in any other infinite dimensional factor, and any infinite dimensional factor contained in R is isomorphic to R.
The outer automorphism group of R is an infinite simple group with countable many conjugacy classes, indexed by pairs consisting of a positive integer p and a complex pth root of 1.
The projections of the hyperfinite II1 factor form a continuous geometry.
While there are other factors of type II∞, there is a unique hyperfinite one, up to isomorphism. It consists of those infinite square matrices with entries in the hyperfinite type II1 factor that define bounded operators.
...
Wikipedia