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In mathematics the spin group Spin is the double cover of the special orthogonal group SO = SO, such that there exists a short exact sequence of Lie groups
As a Lie group, Spin therefore shares its dimension, n/2, and its Lie algebra with the special orthogonal group.
For n > 2, Spin is simply connected and so coincides with the universal cover of SO.
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.
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