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"In mathematics the spin group Spin(n) 1[2] 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)." taken from wikipedia

How to prove that $ Spin(n) $ exists for any $ n $ .

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yes that's what i wanted – Koushik Jan 23 '13 at 11:13
    
See Compact Lie groups by Sepanski – Vishal Gupta Nov 20 '13 at 9:52

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