Extension
If G arises as the group of units of a ring A, then an inner automorphism on G can be extended to a projectivity on the projective space over A by inversive ring geometry. In particular, the inner automorphisms of the classical linear groups can be so extended.
Read more about this topic: Inner Automorphism
Famous quotes containing the word extension:
“The desert is a natural extension of the inner silence of the body. If humanity’s language, technology, and buildings are an extension of its constructive faculties, the desert alone is an extension of its capacity for absence, the ideal schema of humanity’s disappearance.”
—Jean Baudrillard (b. 1929)
“Predatory capitalism created a complex industrial system and an advanced technology; it permitted a considerable extension of democratic practice and fostered certain liberal values, but within limits that are now being pressed and must be overcome. It is not a fit system for the mid- twentieth century.”
—Noam Chomsky (b. 1928)
“A dense undergrowth of extension cords sustains my upper world of lights, music, and machines of comfort.”
—Mason Cooley (b. 1927)