Indefinite Form
There are as many as eight different double covers of O(p, q), for p, q ≠ 0, which correspond to the extensions of the center (which is either C2 × C2 or C4) by C2. Only two of them are pin groups—those that admit the Clifford algebra as a representation. They are called Pin(p, q) and Pin(q, p) respectively.
Read more about this topic: Pin Group
Famous quotes containing the words indefinite and/or form:
“For me chemistry represented an indefinite cloud of future potentialities which enveloped my life to come in black volutes torn by fiery flashes, like those which had hidden Mount Sinai. Like Moses, from that cloud I expected my law, the principle of order in me, around me, and in the world.... I would watch the buds swell in spring, the mica glint in the granite, my own hands, and I would say to myself: “I will understand this, too, I will understand everything.””
—Primo Levi (1919–1987)
“Freedom is the essence of this faith. It has for its object simply to make men good and wise. Its institutions then should be as flexible as the wants of men. That form out of which the life and suitableness have departed should be as worthless in its eyes as the dead leaves that are falling around us.”
—Ralph Waldo Emerson (1803–1882)