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:
“‘Tis the perception of the beautiful,
A fine extension of the faculties,
Platonic, universal, wonderful,
Drawn from the stars, and filtered through the skies,
Without which life would be extremely dull.”
—George Gordon Noel Byron (1788–1824)
“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)
“We know then the existence and nature of the finite, because we also are finite and have extension. We know the existence of the infinite and are ignorant of its nature, because it has extension like us, but not limits like us. But we know neither the existence nor the nature of God, because he has neither extension nor limits.”
—Blaise Pascal (1623–1662)