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.
Read more about this topic: Projective Unitary Group
Famous quotes containing the words special and/or group:
“Fashions change, and with the new psychoanalytical perspective of the postwar period [WWII], child rearing became enshrined as the special responsibility of mothers ... any shortcoming in adult life was now seen as rooted in the failure of mothering during childhood.”
—Sylvia Ann Hewitt (20th century)
“Even in harmonious families there is this double life: the group life, which is the one we can observe in our neighbour’s household, and, underneath, another—secret and passionate and intense—which is the real life that stamps the faces and gives character to the voices of our friends. Always in his mind each member of these social units is escaping, running away, trying to break the net which circumstances and his own affections have woven about him.”
—Willa Cather (1873–1947)