In mathematics, the pin group is a certain subgroup of the Clifford algebra associated to a quadratic space. It maps 2-to-1 to the orthogonal group, just as the spin group maps 2-to-1 to the special orthogonal group.
In general the map from the Pin group to the orthogonal group is not onto or a universal covering space, but if the quadratic form is definite (and dimension is greater than 2), it is both.
The non-trivial element of the kernel is denoted −1, which should not be confused with the orthogonal transform of reflection through the origin, generally denoted −I.
Read more about Pin Group: Definite Form, Indefinite Form, As Topological Group, Construction, Center, Name
Famous quotes containing the words pin and/or group:
“It is not, truly speaking, the labour that is divided; but the men: divided into mere segments of men—broken into small fragments and crumbs of life, so that all the little piece of intelligence that is left in a man is not enough to make a pin, or a nail, but exhausts itself in making the point of a pin or the head of a nail.”
—John Ruskin (1819–1900)
“If the Russians have gone too far in subjecting the child and his peer group to conformity to a single set of values imposed by the adult society, perhaps we have reached the point of diminishing returns in allowing excessive autonomy and in failing to utilize the constructive potential of the peer group in developing social responsibility and consideration for others.”
—Urie Bronfenbrenner (b. 1917)