The projective special unitary group is the group obtained from the special unitary group on factoring by the scalar matrices contained in that group. is simple except for
(1)
 
(2)
 
(3)

so it is given the simpler name , with .
The projective special unitary group is the group obtained from the special unitary group on factoring by the scalar matrices contained in that group. is simple except for
(1)
 
(2)
 
(3)

so it is given the simpler name , with .
Weisstein, Eric W. "Projective Special Unitary Group." From MathWorldA Wolfram Web Resource. https://mathworld.wolfram.com/ProjectiveSpecialUnitaryGroup.html