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 humanitys 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 humanitys disappearance.”
—Jean Baudrillard (b. 1929)
“Slavery is founded on the selfishness of mans natureopposition 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 (18091865)
“We are now a nation of people in daily contact with strangers. Thanks to mass transportation, school administrators and teachers often live many miles from the neighborhood schoolhouse. They are no longer in daily informal contact with parents, ministers, and other institution leaders . . . [and are] no longer a natural extension of parental authority.”
—James P. Comer (20th century)