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

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- May 13th 2011, 09:39 AMalexandrabel90centre
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 - May 13th 2011, 07:10 PMDrexel28
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?