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)
“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.”
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—Abraham Lincoln (1809–1865)