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About LinkBackswhy 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 groupOriginally Posted by alexandrabel90
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?
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