Properties
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.
Read more about this topic: Hyperfinite Type II Factor
Famous quotes containing the word properties:
“A drop of water has the properties of the sea, but cannot exhibit a storm. There is beauty of a concert, as well as of a flute; strength of a host, as well as of a hero.”
—Ralph Waldo Emerson (1803–1882)
“The reason why men enter into society, is the preservation of their property; and the end why they choose and authorize a legislative, is, that there may be laws made, and rules set, as guards and fences to the properties of all the members of the society: to limit the power, and moderate the dominion, of every part and member of the society.”
—John Locke (1632–1704)