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:
“Who wants to become a writer? And why? Because it’s the answer to everything. To “Why am I here?” To uselessness. It’s the streaming reason for living. To note, to pin down, to build up, to create, to be astonished at nothing, to cherish the oddities, to let nothing go down the drain, to make something, to make a great flower out of life, even if it’s a cactus.”
—Enid Bagnold (1889–1981)
“He hung out of the window a long while looking up and down the street. The world’s second metropolis. In the brick houses and the dingy lamplight and the voices of a group of boys kidding and quarreling on the steps of a house opposite, in the regular firm tread of a policeman, he felt a marching like soldiers, like a sidewheeler going up the Hudson under the Palisades, like an election parade, through long streets towards something tall white full of colonnades and stately. Metropolis.”
—John Dos Passos (1896–1970)