In mathematics the spin group Spin(n) is the double cover of the special orthogonal group SO(n), such that there exists a short exact sequence of Lie groups
As a Lie group Spin(n) therefore shares its dimension, n (n − 1)/2, and its Lie algebra with the special orthogonal group. For n > 2 , Spin(n) is simply connected and so coincides with the universal cover of SO(n).
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 .
Spin(n) can be constructed as a subgroup of the invertible elements in the Clifford algebra Cℓ(n).
Read more about Spin Group: Accidental Isomorphisms, Indefinite Signature, Topological Considerations, Center, Quotient Groups, Discrete Subgroups
Famous quotes containing the words spin and/or group:
“Words can have no single fixed meaning. Like wayward electrons, they can spin away from their initial orbit and enter a wider magnetic field. No one owns them or has a proprietary right to dictate how they will be used.”
—David Lehman (b. 1948)
“It’s important to remember that feminism is no longer a group of organizations or leaders. It’s the expectations that parents have for their daughters, and their sons, too. It’s the way we talk about and treat one another. It’s who makes the money and who makes the compromises and who makes the dinner. It’s a state of mind. It’s the way we live now.”
—Anna Quindlen (20th century)