In mathematics, and more specifically in the theory of von Neumann algebras, a crossed product is a basic method of constructing a new von Neumann algebra from a von Neumann algebra acted on by a group. It is related to the semidirect product construction for groups. (Roughly speaking, crossed product is the expected structure for a group ring of a semidirect product group. Therefore crossed products have a ring theory aspect also. This article concentrates on an important case, where they appear in functional analysis.)
Read more about Crossed Product: Motivation, Construction, Properties, Duality, Examples
Famous quotes containing the words crossed and/or product:
“We crossed a deep and wide bay which makes eastward north of Kineo, leaving an island on our left, and keeping to the eastern side of the lake. This way or that led to some Tomhegan or Socatarian stream, up which the Indian had hunted, and whither I longed to go. The last name, however, had a bogus sound, too much like sectarian for me, as if a missionary had tampered with it; but I knew that the Indians were very liberal. I think I should have inclined to the Tomhegan first.”
—Henry David Thoreau (1817–1862)
“These facts have always suggested to man the sublime creed that the world is not the product of manifold power, but of one will, of one mind; and that one mind is everywhere active, in each ray of the star, in each wavelet of the pool; and whatever opposes that will is everywhere balked and baffled, because things are made so, and not otherwise.”
—Ralph Waldo Emerson (1803–1882)