why is it we say that the centre of SU(N) is isomorphic to Z (mod n) and center of U(N) is isomorphic to U(1) when
both their centres are {aI : lal=1}
are they different or the same
Well it's almost always true (as a rule of thumb--not a theorem) that given a (complex, although more general fields of characteristic zero work) matrix group one has that and this is true for so that . That said, we know that since it's true that so that (this is a common notation for the roots of unity) and moreover you can check that for every so that but it's basic group theory that . Does that help?