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I have many questions about the special Orthogonal Group SO(n) and the Special Unitary Group SU(n). The first, SO(n) has [tex]\frac {n (n-1)}{n}[/tex] parameters or degrees of freedom, and the second, SU(n) has [tex] n^2 -1[/tex].

If I take for example the group SO(3), this has 3 degrees of freedom, and SU(2) has too 3 degrees of freedom, and theres a relation 2->1 from SO to SU. The question is, if SU(n) can describe the same that SO(n) or if there's a lose of information in using SU(n).

Best Reggards.

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# Questions aboug Special Groups SO(n) and SU(n)

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