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Spinor group
In mathematics the spinor group Spin(n) is a particular double cover of the special orthogonal group SO(n, R). That is, there exists a short exact sequence of Lie groups
For n > 2, Spin(n) is simply connected and so coincides with the universal cover of SO(n, R). As a Lie group Spin(n) therefore shares its dimension n(n - 1) / 2 and its Lie algebra with the special orthogonal group.
Spin(n) can be constructed as a subgroup of the invertible elements in the Clifford algebra C(n).
See also: spinor, spinor bundle, anyon
10-26-2009 08:16:03
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The contents of this article is licensed from www.wikipedia.org under the GNU Free Documentation License. Click here to see the transparent copy and copyright details