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:
“In tragic life, God wot,
No villain need be! Passions spin the plot:
We are betrayed by what is false within.”
—George Meredith (1828–1909)
“Once it was a boat, quite wooden
and with no business, no salt water under it
and in need of some paint. It was no more
than a group of boards. But you hoisted her, rigged her.
She’s been elected.”
—Anne Sexton (1928–1974)