Projective Special Unitary Group
The projective special unitary group PSU(n) is equal to the projective unitary group, in contrast to the orthogonal case.
The connections between the U(n), SU(n), their centers, and the projective unitary groups is shown at right.
The center of the special unitary group is the scalar matrices of the nth roots of unity:
The natural map
is an isomorphism, by the second isomorphism theorem, thus
- PU(n) = PSU(n) = SU(n)/(Z/n).
and the special unitary group SU(n) is an n-fold cover of the projective unitary group.
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