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:
“A dense undergrowth of extension cords sustains my upper world of lights, music, and machines of comfort.”
—Mason Cooley (b. 1927)
“Slavery is founded in the selfishness of man’s nature—opposition to it, is [in?] his love of justice.... Repeal the Missouri compromise—repeal all compromises—repeal the declaration of independence—repeal all past history, you still can not repeal human nature. It still will be the abundance of man’s heart, that slavery extension is wrong; and out of the abundance of his heart, his mouth will continue to speak.”
—Abraham Lincoln (1809–1865)
“Slavery is founded on the selfishness of man’s nature—opposition to it on his love of justice. These principles are in eternal antagonism; and when brought into collision so fiercely as slavery extension brings them, shocks and throes and convulsions must ceaselessly follow.”
—Abraham Lincoln (1809–1865)